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WACE Maths Applications study materials
WACE Maths Applications study resources

WACE Maths Applications practice questions

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Question 1Mathematics Applications

A dataset of 10 values has a mean of 24. If one value of 14 is removed, what is the new mean of the remaining 9 values?

  1. 25.11 Correct answer.
  2. 24
  3. 26
  4. 23

Explanation

The total of all ten values is 10 × 24 = 240. Removing 14 leaves 226 spread over 9 values, giving 226 ÷ 9 ≈ 25.11. The mean rises because the removed value lies below the original mean.

Question 2Mathematics Applications

The median of a set of 8 ordered data values is found by taking the average of which pair of values?

  1. The 3rd and 6th values
  2. The 4th and 5th values Correct answer.
  3. The 1st and 8th values
  4. The 4th and 8th values

Explanation

For an even number of ordered values the median lies halfway between the two central values. With 8 values the central positions are the 4th and 5th. Their average splits the data into two equal halves.

Question 3Mathematics Applications

A set of data has an interquartile range of 12 and a lower quartile of 30. A value of 8 is recorded. Using the standard 1.5 × IQR rule, is this value an outlier?

  1. No, because 8 lies inside the quartile range
  2. Yes, because 8 is below the lower fence of 6
  3. No, because 8 is above the lower fence of 12
  4. Yes, because 8 is below the lower fence of 12 Correct answer.

Explanation

The lower fence equals Q1 − 1.5 × IQR = 30 − 18 = 12. Any value below 12 is flagged as an outlier, and 8 is below 12. The upper fence would be 30 + 12 + 18 = 60, which is irrelevant here.

Question 4Mathematics Applications

A scatterplot shows a strong negative linear association between two variables. Which statement best describes the correlation coefficient r?

  1. r is close to 0
  2. r is close to −1 Correct answer.
  3. r is exactly 0
  4. r is close to +1

Explanation

The sign of r matches the direction of the association, so a negative trend gives a negative r. A strong linear pattern means the magnitude is near 1, so r is close to −1. Values near 0 indicate weak linear association.

Question 5Mathematics Applications

A least-squares regression line is y = 3.2x + 15. What does the slope of 3.2 represent?

  1. The predicted increase in y for each one-unit increase in x Correct answer.
  2. The predicted value of y when x equals zero
  3. The value of x when y equals zero
  4. The strength of the linear association

Explanation

In a linear model y = mx + c the gradient m gives the change in the response for each unit change in the explanatory variable. Here y is predicted to rise by 3.2 whenever x rises by 1. The intercept, not the slope, gives the value at x = 0.

Question 6Mathematics Applications

A residual plot from a linear regression shows a clear curved pattern. What does this suggest?

  1. A linear model may not be appropriate Correct answer.
  2. The data contain no outliers
  3. The slope must be negative
  4. The correlation is exactly zero

Explanation

Residuals should be scattered randomly about zero if a straight line fits well. A systematic curved pattern shows the model is missing a nonlinear trend. In that case a different form of model should be considered.

Question 7Mathematics Applications

A quantity grows by 6% each year. Which expression gives its value after 5 years if it starts at P?

  1. P × 1.06 × 5
  2. P × (1 + 0.06 × 5)
  3. P × 0.94^5
  4. P × 1.06^5 Correct answer.

Explanation

Repeated percentage growth is multiplicative, so each year multiplies the amount by 1.06. After five years the multiplier 1.06 is applied five times, giving P × 1.06^5. This is compound growth rather than simple growth.

Question 8Mathematics Applications

An item costing $80 is reduced by 25% in a sale. What is the sale price?

  1. $55
  2. $100
  3. $20
  4. $60 Correct answer.

Explanation

A 25% reduction leaves 75% of the original price. Multiplying $80 by 0.75 gives $60. Alternatively, the discount is $20, and subtracting it from $80 gives $60.

Question 9Mathematics Applications

A car travels 150 km in 2 hours and then 90 km in 1 hour. What is its average speed for the whole journey?

  1. 75 km/h
  2. 120 km/h
  3. 80 km/h Correct answer.
  4. 85 km/h

Explanation

Average speed is total distance divided by total time. The total distance is 150 + 90 = 240 km and the total time is 3 hours. Dividing gives 240 ÷ 3 = 80 km/h.

Question 10Mathematics Applications

A recipe for 6 people requires 450 g of flour. How much flour is needed for 10 people at the same rate?

  1. 675 g
  2. 270 g
  3. 750 g Correct answer.
  4. 900 g

Explanation

The amount per person is 450 ÷ 6 = 75 g. Scaling to 10 people gives 75 × 10 = 750 g. Setting up the proportion 450/6 = x/10 gives the same result.

Question 11Mathematics Applications

Two workers can complete a task in 12 days. How long would it take five workers, assuming they work at the same constant rate?

  1. 6 days
  2. 2.4 days
  3. 30 days
  4. 4.8 days Correct answer.

Explanation

The total work equals 2 × 12 = 24 worker-days. Dividing this by 5 workers gives 24 ÷ 5 = 4.8 days. More workers means less time, so the quantities are inversely proportional.

Question 12Mathematics Applications

A map has a scale of 1 : 25 000. A distance of 6 cm on the map represents what actual distance?

  1. 15 km
  2. 0.15 km
  3. 150 km
  4. 1.5 km Correct answer.

Explanation

Each centimetre represents 25 000 cm, so 6 cm represents 150 000 cm. Converting to metres gives 1500 m, and converting to kilometres gives 1.5 km.

Question 13Mathematics Applications

A right-angled triangle has an opposite side of 8 and a hypotenuse of 17. What is the length of the adjacent side?

  1. 9
  2. 12
  3. 15 Correct answer.
  4. 25

Explanation

Pythagoras' theorem gives adjacent² = 17² − 8² = 289 − 64 = 225. Taking the positive square root gives 15. The triangle is a scaled 8-15-17 triple.

Question 14Mathematics Applications

In a right-angled triangle the angle is 35° and the hypotenuse is 20 cm. What is the length of the side opposite the angle, to one decimal place?

  1. 28.6 cm
  2. 14.0 cm
  3. 11.5 cm Correct answer.
  4. 16.4 cm

Explanation

The sine ratio links the opposite side and the hypotenuse: sin 35° = opposite ÷ 20. Rearranging gives opposite = 20 × sin 35° ≈ 20 × 0.5736 ≈ 11.5 cm.

Question 15Mathematics Applications

A bearing is measured in which way?

  1. From the nearest compass point, up to 90°
  2. Clockwise from north, between 0° and 360° Correct answer.
  3. Counter-clockwise from north, between 0° and 360°
  4. Clockwise from east, between 0° and 360°

Explanation

A true bearing is always stated as three digits measured clockwise from north. It ranges from 000° to 360°, so east is 090° and south is 180°. This convention lets every direction be described uniquely.

Question 16Mathematics Applications

A sine rule calculation gives sin θ = 0.8 for an angle in a triangle. Which pair of possible angles could θ take?

  1. 53.1° only
  2. 53.1° or 306.9°
  3. 36.9° or 143.1°
  4. 53.1° or 126.9° Correct answer.

Explanation

The sine ratio is positive in the first and second quadrants. The inverse sine of 0.8 is about 53.1°, and the supplementary angle is 180° − 53.1° = 126.9°. Both can occur in a triangle, giving the ambiguous case.

Question 17Mathematics Applications

A loan of $5000 is taken at a flat interest rate of 8% per annum for 3 years. What is the total simple interest charged?

  1. $1298.56
  2. $1200 Correct answer.
  3. $3600
  4. $400

Explanation

Simple interest is I = P × r × t = 5000 × 0.08 × 3. This equals 5000 × 0.24 = $1200. The interest is calculated on the original principal each year.

Question 18Mathematics Applications

$2000 is invested at 5% per annum compounded annually. What is the value after 3 years, to the nearest dollar?

  1. $2315 Correct answer.
  2. $2300
  3. $2150
  4. $2431

Explanation

Compound growth uses the multiplier 1.05 applied three times. So the value is 2000 × 1.05³ = 2000 × 1.157625 ≈ $2315. The interest is earned on interest as well as on the principal.

Question 19Mathematics Applications

A depreciation model uses the recurrence relation V(n+1) = 0.85 V(n), with V(0) = 40 000. What does the value 0.85 represent?

  1. The value halves every 0.85 years
  2. The value increases by 85% each year
  3. The value loses $85 each year
  4. The value retains 85% of its previous value each year Correct answer.

Explanation

In a recurrence of the form V(n+1) = r V(n), the multiplier r gives the fraction carried forward. A multiplier of 0.85 means 85% remains, so the item loses 15% of its value each year.

Question 20Mathematics Applications

A recurrence relation is t(n+1) = 2 t(n) + 3 with t(1) = 4. What is t(3)?

  1. 22
  2. 14
  3. 11
  4. 25 Correct answer.

Explanation

Apply the rule step by step. First t(2) = 2 × 4 + 3 = 11, then t(3) = 2 × 11 + 3 = 25. Each term depends on the previous one, so the order of evaluation matters.

Question 21Mathematics Applications

A geometric sequence has first term 5 and common ratio 3. What is the 4th term?

  1. 405
  2. 60
  3. 45
  4. 135 Correct answer.

Explanation

The nth term of a geometric sequence is a × r^(n−1). Here the 4th term is 5 × 3³ = 5 × 27 = 135. Each term is three times the previous term.

Question 22Mathematics Applications

A linear programming feasible region is bounded by the vertices (0, 0), (4, 0), (2, 5) and (0, 3). The objective function is P = 3x + 2y. At which vertex is P maximised?

  1. (2, 5) Correct answer.
  2. (0, 0)
  3. (4, 0)
  4. (0, 3)

Explanation

Evaluate P at each vertex: (0,0) gives 0, (4,0) gives 12, (2,5) gives 16, and (0,3) gives 6. The largest value is 16 at (2, 5). For a linear objective the optimum always occurs at a vertex.

Question 23Mathematics Applications

A network has four vertices A, B, C and D with edges AB, BC, CD and DA. What type of graph is this?

  1. A complete graph
  2. A graph with an isolated vertex
  3. A cycle of length 4 Correct answer.
  4. A tree with four edges

Explanation

Each vertex has degree 2, and the edges form a closed loop A–B–C–D–A. A closed loop is a cycle, and here it passes through four vertices. Trees contain no cycles, and complete graphs have every pair connected.

Question 24Mathematics Applications

A project network has activities with durations A = 4 days, B = 6 days and C = 3 days. A must finish before B starts, and B must finish before C starts. What is the earliest completion time of the project?

  1. 7 days
  2. 10 days
  3. 13 days Correct answer.
  4. 9 days

Explanation

The activities form a single chain, so their durations add along the path. The total is 4 + 6 + 3 = 13 days. No activity can start before its predecessor finishes.

Question 25Mathematics Applications

In a set of 20 scores, the 5th and 6th ordered values are both 62, and the 15th and 16th ordered values are both 78. What is the interquartile range?

  1. 8
  2. 16 Correct answer.
  3. 62
  4. 78

Explanation

With 20 values the lower quartile is the median of the lower ten, falling between the 5th and 6th values, so Q1 = 62. The upper quartile falls between the 15th and 16th values, so Q3 = 78. The interquartile range is 78 − 62 = 16.

Question 26Mathematics Applications

A set of 9 ordered data values is given. Which value is the median?

  1. The 5th value Correct answer.
  2. The 4.5th value
  3. The 9th value
  4. The 4th value

Explanation

The median is the middle value once the data are placed in order. With 9 values there are 4 below and 4 above, so the middle position is the 5th value.

Question 27Mathematics Applications

A data set has mean 50 and standard deviation 5. A value of 62 is recorded. What is its standardised z-score?

  1. 1.2
  2. 12
  3. 2.4 Correct answer.
  4. 0.24

Explanation

A z-score measures how many standard deviations a value lies from the mean, computed as (x − mean) ÷ standard deviation. Here (62 − 50) ÷ 5 = 2.4, so the value is 2.4 standard deviations above the mean.

Question 28Mathematics Applications

A scatterplot of two variables shows points tightly clustered around a straight line with negative slope. Which statement best describes the association?

  1. Strong positive linear association
  2. Weak positive linear association
  3. No association at all
  4. Strong negative linear association Correct answer.

Explanation

Tight clustering about a straight line indicates a strong linear association, and a downward slope means that as one variable increases the other decreases. Together these describe a strong negative linear association.

Question 29Mathematics Applications

A trend line fitted to data is y = 3.2x + 15. What does the value 3.2 represent?

  1. The predicted increase in y for each one-unit increase in x Correct answer.
  2. The predicted value of y when x equals zero
  3. The strength of the linear association
  4. The total change in y across the whole data set

Explanation

In a linear model y = mx + c, the gradient m gives the rate of change of the response with respect to the explanatory variable. So 3.2 is the predicted change in y per one-unit increase in x.

Question 30Mathematics Applications

A seasonal index for summer sales is 1.15. What does this indicate?

  1. Summer sales are typically 15% above the overall average Correct answer.
  2. Summer sales are typically 15% below the overall average
  3. Summer sales are 115% below the overall average
  4. Summer sales equal the overall average

Explanation

A seasonal index compares the value in a season with the overall average, where an index of 1 means equal to the average. An index of 1.15 means the season is 0.15, or 15%, above the average.

Question 31Mathematics Applications

A recurrence relation models a reducing-balance loan: B(n+1) = 1.005 B(n) − 400. What does the 400 represent?

  1. The monthly interest rate
  2. The regular repayment made each period Correct answer.
  3. The amount originally borrowed
  4. The number of repayment periods

Explanation

In a reducing-balance recurrence the balance is increased by the interest factor and then reduced by the payment. The constant subtracted each period, 400, is therefore the regular repayment amount.

Question 32Mathematics Applications

Which statement about a planar graph is always true?

  1. It must be a complete graph
  2. It must contain a cycle
  3. Every vertex must have even degree
  4. It can be drawn on a flat surface with no edges crossing Correct answer.

Explanation

A planar graph is defined by the property that it can be drawn in a plane so that edges meet only at vertices. Crossing edges can be avoided by redrawing, which is the defining feature.

Question 33Mathematics Applications

A path in a network passes through vertices A, B, C, D and returns to A without repeating any other vertex. What is this structure called?

  1. A bridge
  2. A tree
  3. A loop
  4. A cycle Correct answer.

Explanation

A closed route that starts and ends at the same vertex and visits no other vertex twice is a cycle. Returning to the starting point is the key feature that distinguishes it from a simple path.

Question 34Mathematics Applications

A quantity is measured as 48.6 with an absolute error of 0.3. What is the percentage error, to one decimal place?

  1. 0.3%
  2. 0.6% Correct answer.
  3. 6.2%
  4. 1.6%

Explanation

Percentage error is the absolute error divided by the measured value, then multiplied by 100. Here 0.3 ÷ 48.6 × 100 ≈ 0.617%, which rounds to 0.6%.

Question 35Mathematics Applications

A car's fuel use is 8.4 litres per 100 km. How many litres are needed for a journey of 350 km?

  1. 21.0 L
  2. 35.0 L
  3. 29.4 L Correct answer.
  4. 42.0 L

Explanation

Set up a proportion: litres per kilometre is 8.4 ÷ 100 = 0.084. Multiplying by 350 km gives 0.084 × 350 = 29.4 litres.

Question 36Mathematics Applications

A plan uses a scale of 1 : 500. A rectangular room measures 8 cm by 6 cm on the plan. What is the actual area of the room in square metres?

  1. 120 m²
  2. 1200 m² Correct answer.
  3. 480 m²
  4. 48 m²

Explanation

Each 1 cm on the plan represents 500 cm, or 5 m, so the room is 40 m by 30 m. The actual area is 40 × 30 = 1200 square metres.

Question 37Mathematics Applications

A right-angled triangle has an adjacent side of 9 cm and an angle of 40° at that side. What is the length of the hypotenuse, to one decimal place?

  1. 7.0 cm
  2. 5.8 cm
  3. 11.7 cm Correct answer.
  4. 14.0 cm

Explanation

The cosine ratio links the adjacent side and the hypotenuse: cos 40° = 9 ÷ hypotenuse. Rearranging gives hypotenuse = 9 ÷ cos 40° ≈ 9 ÷ 0.766 ≈ 11.7 cm.

Question 38Mathematics Applications

A ship sails 12 km on a bearing of 090° and then 5 km on a bearing of 180°. How far is it from its starting point?

  1. 13 km Correct answer.
  2. 8.5 km
  3. 7 km
  4. 17 km

Explanation

The two legs are perpendicular: east then south, so they form a right angle. Using Pythagoras, distance = √(12² + 5²) = √169 = 13 km.

Question 39Mathematics Applications

An investment of $4000 earns 6% per annum compounded quarterly. Which expression gives its value after 2 years?

  1. 4000 × (1 + 0.06/2)^4
  2. 4000 × (1 + 0.06)^2
  3. 4000 × (1 + 0.06/4)^8 Correct answer.
  4. 4000 × (1 + 0.06/4)^2

Explanation

Quarterly compounding divides the annual rate by 4 and applies it 4 times per year. Over 2 years there are 8 compounding periods, giving 4000 × (1.015)^8.

Question 40Mathematics Applications

A recurrence relation is V(n+1) = 0.9 V(n) + 200, with V(0) = 1000. What is V(2)?

  1. 1290
  2. 1010
  3. 1190 Correct answer.
  4. 1100

Explanation

Apply the relation step by step: V(1) = 0.9 × 1000 + 200 = 1100, then V(2) = 0.9 × 1100 + 200 = 1190. Each step multiplies by 0.9 then adds 200.

Question 41Mathematics Applications

A linear programming problem has feasible region with vertices (0,0), (5,0), (3,4) and (0,2). The objective P = 2x + 3y is to be maximised. What is the maximum value?

  1. 10
  2. 13
  3. 16
  4. 18 Correct answer.

Explanation

Evaluate P at each vertex: (0,0) gives 0, (5,0) gives 10, (3,4) gives 6 + 12 = 18, and (0,2) gives 6. The maximum is 18 at the vertex (3,4).

Question 42Mathematics Applications

A project has activities with earliest start times: A = 0, B = 4, C = 7. Their durations are A = 4, B = 6, C = 3, and all three must finish before the project ends. What is the project's minimum completion time?

  1. 13 days
  2. 7 days
  3. 14 days
  4. 10 days Correct answer.

Explanation

Each activity finishes at its earliest start plus its duration: A ends at 4, B ends at 10, C ends at 10. The project completes when all finish, so the minimum time is 10 days.

Question 43Mathematics Applications

A graph has 6 vertices and 9 edges. How many edges must be removed to obtain a spanning tree?

  1. 2
  2. 3
  3. 4 Correct answer.
  4. 5

Explanation

A spanning tree on 6 vertices has exactly 5 edges, since a tree on n vertices has n − 1 edges. Removing 9 − 5 = 4 edges therefore yields a spanning tree.

Question 44Mathematics Applications

A set of data has a lower quartile of 22 and an upper quartile of 38. Using the 1.5 × IQR rule, what is the upper fence for outliers?

  1. 46
  2. 54
  3. 60
  4. 62 Correct answer.

Explanation

The interquartile range is 38 − 22 = 16, and 1.5 × 16 = 24. The upper fence is the upper quartile plus this value, 38 + 24 = 62.

Question 45Mathematics Applications

A time series has actual value 240 and a centred four-point moving average of 200. What is the seasonal index for that period, to two decimal places?

  1. 1.20 Correct answer.
  2. 0.83
  3. 0.60
  4. 1.40

Explanation

A seasonal index is the actual value divided by the moving average for that period. Here 240 ÷ 200 = 1.20, indicating the period is 20% above the trend.

Question 46Mathematics Applications

Two variables have a correlation coefficient of r = −0.92. A student concludes that changes in the first variable cause changes in the second. Which statement is the best response?

  1. The correlation is too weak to support any conclusion
  2. The association is strong and negative, but causation cannot be inferred from correlation alone Correct answer.
  3. The conclusion is valid because the correlation is close to −1
  4. The conclusion is invalid only because the correlation is negative

Explanation

A correlation of −0.92 indicates a strong negative linear association, but correlation measures only the strength of a relationship. It cannot establish that one variable causes the other, because lurking variables may be responsible.

Question 47Mathematics Applications

A reducing-balance loan of $20 000 at 0.8% per month is repaid with monthly payments of $500. Which statement about the loan balance is correct?

  1. The balance rises each month because interest is compounded
  2. The balance stays constant because the payment equals the interest
  3. The balance falls each month because the payment exceeds the monthly interest Correct answer.
  4. The balance falls only after the interest rate is reduced

Explanation

Monthly interest on $20 000 at 0.8% is $160, which is less than the $500 payment. Since each payment exceeds the interest charged, the balance decreases every month.

Question 48Mathematics Applications

A recurrence relation is t(n+1) = 3 t(n) − 4, with t(1) = 3. Which expression gives the fixed point of this recurrence?

  1. 3
  2. 1
  3. 4
  4. 2 Correct answer.

Explanation

A fixed point satisfies t = 3t − 4, since the value does not change from one term to the next. Solving gives 2t = 4, so t = 2.

Question 49Mathematics Applications

In a linear programming problem, the objective P = 4x + 5y is to be maximised over a feasible region, and the vertices are (0,0), (6,0), (4,3) and (0,5). Which vertex gives the maximum, and what is its value?

  1. (4,3) with P = 31 Correct answer.
  2. (0,5) with P = 25
  3. (0,0) with P = 0
  4. (6,0) with P = 24

Explanation

Evaluate P at each vertex: (0,0) gives 0, (6,0) gives 24, (4,3) gives 16 + 15 = 31, and (0,5) gives 25. The largest value is 31 at (4,3).

Question 50Mathematics Applications

A network is connected and every vertex has even degree. Which conclusion follows?

  1. The network must be a tree
  2. Every vertex must have degree two
  3. The network cannot be traversed without repeating edges
  4. An Eulerian circuit exists that traverses every edge exactly once Correct answer.

Explanation

Euler's theorem states that a connected graph has an Eulerian circuit if and only if every vertex has even degree. Such a circuit uses every edge exactly once and returns to the start.