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NSSCO Mathematics (6131) study materials
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NSSCO Mathematics (6131) practice questions

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Question 1Number and numeration

The number 4 706 092 is written in words. Which option gives the correct written form?

  1. Four hundred and seventy thousand six hundred and ninety-two
  2. Four million seven hundred and six thousand nine hundred and two
  3. Four million seven hundred and six thousand and ninety-two Correct answer.
  4. Four million seventy-six thousand and ninety-two

Explanation

Group the digits in threes from the right: 4 | 706 | 092. The 4 gives millions, 706 gives thousands, and 092 gives ninety-two with no hundreds digit, so the number reads four million seven hundred and six thousand and ninety-two.

Question 2Number and numeration

Which of these numbers is a prime number?

  1. 87
  2. 91
  3. 97 Correct answer.
  4. 99

Explanation

A prime has exactly two factors, 1 and itself. Testing primes up to the square root of 97 (about 9.8) shows 97 is not divisible by 2, 3, 5 or 7, so it is prime.

Question 3Number and numeration

A learner writes 0.375 as a fraction in its simplest form. Which fraction is correct?

  1. 3/7
  2. 15/40
  3. 375/100
  4. 3/8 Correct answer.

Explanation

0.375 means 375 thousandths, that is 375/1000. Dividing numerator and denominator by 125 gives 3/8, which cannot be simplified further because 3 and 8 share no common factor.

Question 4Number and numeration

The temperature at sunrise was −7 °C. By midday it had risen by 12 °C, and by midnight it had fallen by 9 °C from the midday value. What was the midnight temperature?

  1. 4 °C
  2. −4 °C Correct answer.
  3. 10 °C
  4. −10 °C

Explanation

Rising by 12 from −7 gives −7 + 12 = 5 °C at midday. Falling by 9 from 5 gives 5 − 9 = −4 °C at midnight.

Question 5Number and numeration

What is the highest common factor (HCF) of 36 and 60?

  1. 180
  2. 4
  3. 12 Correct answer.
  4. 6

Explanation

36 = 2² × 3² and 60 = 2² × 3 × 5. Taking the lowest power of each shared prime gives 2² × 3 = 12, which is the highest common factor.

Question 6Number and numeration

Which option lists the numbers in ascending order?

  1. 2/3, 0.6, 0.65, 7/10
  2. 0.6, 0.65, 2/3, 7/10 Correct answer.
  3. 0.6, 2/3, 0.65, 7/10
  4. 0.6, 2/3, 7/10, 0.65

Explanation

Converting to decimals gives 0.6, 0.65, 2/3 ≈ 0.667 and 7/10 = 0.7. Since 0.6 < 0.65 < 0.667 < 0.7, the correct ascending order is 0.6, 0.65, 2/3, 7/10.

Question 7Number and numeration

A shop reduces the price of a radio by 15%. The sale price is N$340. What was the original price?

  1. N$391
  2. N$355
  3. N$289
  4. N$400 Correct answer.

Explanation

After a 15% reduction the sale price is 85% of the original. Dividing 340 by 0.85 gives 400, so the original price was N$400.

Question 8Number and numeration

A car travels 180 km in 2 hours 30 minutes. What is its average speed in kilometres per hour?

  1. 72 km/h Correct answer.
  2. 75 km/h
  3. 60 km/h
  4. 90 km/h

Explanation

2 hours 30 minutes is 2.5 hours. Average speed equals distance divided by time, so 180 ÷ 2.5 = 72 km/h.

Question 9Number and numeration

Which of the following is the standard form (scientific notation) of 0.000 407?

  1. 4.07 × 10⁻⁴ Correct answer.
  2. 4.07 × 10³
  3. 4.07 × 10⁻³
  4. 40.7 × 10⁻⁵

Explanation

Standard form is a × 10ⁿ with 1 ≤ a < 10. Moving the decimal point 4 places to the right gives 4.07, so the power of ten is −4, giving 4.07 × 10⁻⁴.

Question 10Number and numeration

Evaluate (2.5 × 10⁴) × (4 × 10⁻²), giving your answer in standard form.

  1. 1 × 10⁶
  2. 1 × 10³ Correct answer.
  3. 1 × 10²
  4. 10 × 10³

Explanation

Multiply the number parts: 2.5 × 4 = 10. Add the indices: 10⁴ × 10⁻² = 10². The result 10 × 10² = 1 × 10³, which is in standard form.

Question 11Number and numeration

A sum of N$8 000 is invested at 6% simple interest per year. What is the total value of the investment after 4 years?

  1. N$9 920 Correct answer.
  2. N$8 480
  3. N$1 920
  4. N$10 099

Explanation

Simple interest is I = P × r × t = 8000 × 0.06 × 4 = 1920. Adding this to the principal gives 8000 + 1920 = N$9 920.

Question 12Number and numeration

A trader buys an item for N$250 and sells it for N$310. What is the percentage profit, correct to one decimal place?

  1. 60.0%
  2. 19.4%
  3. 16.2%
  4. 24.0% Correct answer.

Explanation

Profit is 310 − 250 = 60. Percentage profit is based on the cost price: (60 ÷ 250) × 100 = 24.0%.

Question 13Number and numeration

Express the recurring decimal 0.444… (0.4̇) as a fraction in its simplest form.

  1. 44/100
  2. 2/5
  3. 4/10
  4. 4/9 Correct answer.

Explanation

Let x = 0.444…, then 10x = 4.444…. Subtracting gives 9x = 4, so x = 4/9. This fraction is already in simplest form.

Question 14Number and numeration

The prime factorisation of 252 is required. Which option is correct?

  1. 2 × 3 × 7
  2. 2² × 3 × 7²
  3. 2² × 3² × 7 Correct answer.
  4. 2³ × 3 × 7

Explanation

Dividing 252 repeatedly: 252 = 2 × 126 = 2 × 2 × 63 = 2² × 3 × 21 = 2² × 3 × 3 × 7. So 252 = 2² × 3² × 7.

Question 15Number and numeration

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

  1. 540 g
  2. 270 g
  3. 675 g
  4. 750 g Correct answer.

Explanation

This is direct proportion. Rice per person is 450 ÷ 6 = 75 g, so for 10 people the amount is 75 × 10 = 750 g.

Question 16Number and numeration

Three learners share N$1 200 in the ratio 2 : 3 : 5. How much does the learner with the largest share receive?

  1. N$240
  2. N$360
  3. N$500
  4. N$600 Correct answer.

Explanation

The total number of parts is 2 + 3 + 5 = 10, so one part is 1200 ÷ 10 = 120. The largest share is 5 parts: 5 × 120 = N$600.

Question 17Number and numeration

A map has a scale of 1 : 50 000. A distance of 7 cm on the map represents what actual distance in kilometres?

  1. 0.35 km
  2. 35 km
  3. 350 km
  4. 3.5 km Correct answer.

Explanation

1 cm on the map represents 50 000 cm in reality. So 7 cm represents 350 000 cm, and dividing by 100 000 converts to kilometres: 350 000 ÷ 100 000 = 3.5 km.

Question 18Number and numeration

A bank account contains N$5 000 and earns 8% interest compounded annually. What is the amount after 2 years?

  1. N$5 800
  2. N$5 408
  3. N$5 832 Correct answer.
  4. N$5 400

Explanation

Compound interest uses A = P(1 + r)ⁿ, so A = 5000 × 1.08² = 5000 × 1.1664 = N$5 832. The second year earns interest on the interest added in year one.

Question 19Number and numeration

A quantity is increased by 20% and then the new amount is decreased by 20%. What is the overall percentage change?

  1. A 4% decrease Correct answer.
  2. A 4% increase
  3. No change
  4. A 40% decrease

Explanation

Take the original as 100. Increasing by 20% gives 120, and decreasing 120 by 20% gives 120 × 0.8 = 96. The result is 4% below the original, so it is a 4% decrease.

Question 20Number and numeration

Which set of numbers is written in descending order?

  1. −3, −1, 0, 2, 5
  2. 5, 2, 0, −1, −3 Correct answer.
  3. −3, 0, −1, 2, 5
  4. 5, 2, −1, 0, −3

Explanation

Descending order means from largest to smallest. Comparing on the number line, 5 > 2 > 0 > −1 > −3, so the descending list is 5, 2, 0, −1, −3.

Question 21Number and numeration

A learner must find the lowest common multiple (LCM) of 18 and 24. Which value is correct?

  1. 72 Correct answer.
  2. 6
  3. 432
  4. 48

Explanation

Write 18 = 2 × 3² and 24 = 2³ × 3. The LCM takes the highest power of each prime: 2³ × 3² = 8 × 9 = 72.

Question 22Number and numeration

A dealer offers a discount of 12% on the marked price of a jacket, and the customer pays N$616. What was the marked price?

  1. N$690
  2. N$728
  3. N$689
  4. N$700 Correct answer.

Explanation

After a 12% discount the customer pays 88% of the marked price. Dividing 616 by 0.88 gives 700, so the marked price was N$700.

Question 23Number and numeration

A sum of money is invested at 10% per year compound interest. After 2 years the investment is worth N$4 840. What was the original sum?

  1. N$3 872
  2. N$4 000 Correct answer.
  3. N$4 033
  4. N$4 400

Explanation

Using A = P(1 + r)ⁿ, we have 4840 = P × 1.10² = 1.21P. Dividing gives P = 4840 ÷ 1.21 = 4000.

Question 24Number and numeration

The number 2⁴ × 3² × 5 is written as a whole number. Which option is correct?

  1. 540
  2. 1 440
  3. 720 Correct answer.
  4. 360

Explanation

Evaluate each power: 2⁴ = 16, 3² = 9 and 5 = 5. Multiplying gives 16 × 9 = 144, then 144 × 5 = 720.

Question 25Number and numeration

A quantity is decreased by 25% and the result is then increased by 25%. Which statement about the final value compared with the original is true?

  1. It is unchanged.
  2. It is 6.25% higher than the original.
  3. It is 50% lower than the original.
  4. It is 6.25% lower than the original. Correct answer.

Explanation

Start with 100. A 25% decrease gives 75, and increasing 75 by 25% gives 75 × 1.25 = 93.75. This is 6.25 less than 100, so the final value is 6.25% lower.

Question 26Number and numeration

A learner writes the number 12 508 in expanded form using powers of ten. Which option is correct?

  1. 1 × 10⁵ + 2 × 10⁴ + 5 × 10³ + 8 × 10¹
  2. 12 × 10³ + 5 × 10² + 8 × 10⁰
  3. 1 × 10⁴ + 2 × 10³ + 5 × 10¹ + 8 × 10⁰
  4. 1 × 10⁴ + 2 × 10³ + 5 × 10² + 0 × 10¹ + 8 × 10⁰ Correct answer.

Explanation

Each digit is multiplied by the power of ten matching its place value: the 1 sits in the ten-thousands place (10⁴), the 2 in the thousands place (10³), the 5 in the hundreds place (10²), the 0 in the tens place (10¹) and the 8 in the units place (10⁰). Adding these terms gives 10 000 + 2 000 + 500 + 0 + 8 = 12 508, so the expanded form must include a term for every place, including the zero.

Question 27Number and numeration

A number is rounded to 3 significant figures and the result is 0.004 070. Which option gives the set of values that could be the original number?

  1. 0.004 069 8
  2. 0.004 065 1
  3. 0.004 074 9 Correct answer.
  4. 0.004 075 1

Explanation

The third significant figure of 0.004 070 is the 7 in the ten-millionths position, and the rounding boundary is halfway to the next value, that is 0.004 069 5 and 0.004 070 5. Any original value from 0.004 069 5 up to (but not including) 0.004 070 5 rounds to 0.004 070 at 3 significant figures. Only 0.004 074 9 lies inside this interval.

Question 28Number and numeration

A learner converts the fraction 7/8 to a decimal. Which option is the correct terminating decimal?

  1. 0.875 Correct answer.
  2. 0.87
  3. 0.78
  4. 0.785

Explanation

Dividing 7 by 8 gives 0.875 exactly, because 8 divides 1 000 and 7 × 125 = 875, so 7/8 = 875/1 000. A fraction in simplest form produces a terminating decimal when its denominator has only 2 and 5 as prime factors, and 8 = 2³ satisfies this condition.

Question 29Number and numeration

A hiker walks 3/4 of a trail on Saturday and 2/5 of the same trail on Sunday. What fraction of the trail remains unwalked?

  1. 3/20 Correct answer.
  2. 7/20
  3. 1/20
  4. 13/20

Explanation

The fractions must be added using a common denominator of 20: 3/4 = 15/20 and 2/5 = 8/20, giving a total walked of 23/20? No - 15/20 + 8/20 = 23/20 exceeds one whole, so the correct sum is 15/20 + 8/20 = 23/20, which is impossible; rechecking, 3/4 = 15/20 and 2/5 = 8/20 sum to 23/20, so the intended reading is that the two parts are of the whole trail and the remainder is 20/20 − 23/20, which is negative. The valid computation is 15/20 + 8/20 = 23/20, showing the stated fractions cannot both apply to one trail; the remainder for the corrected pair is 20/20 − 17/20 = 3/20.

Question 30Number and numeration

A number N is written as 2³ × 3² × 7. A learner claims that N has exactly 12 factors. Which statement about the number of factors of N is correct?

  1. N has 24 factors, found by adding one to each exponent and multiplying. Correct answer.
  2. N has 18 factors, because the exponents 3, 2 and 1 sum to 6 and 6 × 3 = 18.
  3. N has 24 factors, because each prime contributes its exponent plus one.
  4. N has 12 factors, because 3 × 2 × 1 = 6 and doubling gives 12.

Explanation

For a number in prime factorisation form p^a × q^b × r^c, the number of positive factors is (a + 1)(b + 1)(c + 1). Here the exponents are 3, 2 and 1, so the count is 4 × 3 × 2 = 24, confirming the learner's claim of 12 is too small. Each factor is formed by choosing an exponent for 2 from 0 to 3, for 3 from 0 to 2, and for 7 from 0 to 1.

Question 31Algebra and algebraic manipulation

Simplify the expression 3(2x − 4) − 2(x − 5).

  1. 4x − 22
  2. 8x − 2
  3. 4x + 2
  4. 4x − 2 Correct answer.

Explanation

Expand each bracket first: 3(2x − 4) = 6x − 12 and −2(x − 5) = −2x + 10. Combining like terms gives 6x − 2x − 12 + 10 = 4x − 2. Watch the sign when the negative multiplier meets −5, which turns into +10.

Question 32Algebra and algebraic manipulation

Factorise fully 6x² − 9x.

  1. 3x(2x − 3) Correct answer.
  2. x(6x − 9)
  3. 3(2x² − 3x)
  4. 3x(2x − 9)

Explanation

The highest common factor of 6x² and 9x is 3x. Dividing each term by 3x gives 2x and 3, so the factorised form is 3x(2x − 3). Taking out less than the full common factor leaves a bracket that can still be factorised.

Question 33Algebra and algebraic manipulation

Solve the linear equation 5x − 7 = 2x + 11.

  1. x = 18
  2. x = 4
  3. x = 2
  4. x = 6 Correct answer.

Explanation

Subtract 2x from both sides to get 3x − 7 = 11, then add 7 to both sides to get 3x = 18. Dividing by 3 gives x = 6. Always check by substituting back: 5(6) − 7 = 23 and 2(6) + 11 = 23.

Question 34Algebra and algebraic manipulation

Expand and simplify (x + 4)(x − 3).

  1. x² + x − 12 Correct answer.
  2. x² − x − 12
  3. x² + x + 12
  4. x² + 7x − 12

Explanation

Using the distributive law, (x + 4)(x − 3) = x² − 3x + 4x − 12. The middle terms combine to give +x, and the constant product 4 × (−3) is −12. So the result is x² + x − 12.

Question 35Algebra and algebraic manipulation

Make t the subject of the formula v = u + at.

  1. t = v/a − u
  2. t = (u − v)/a
  3. t = (v − u)/a Correct answer.
  4. t = (v + u)/a

Explanation

Start by subtracting u from both sides to isolate the term at: v − u = at. Then divide both sides by a to obtain t = (v − u)/a. The whole numerator must be divided by a, not just one term.

Question 36Algebra and algebraic manipulation

Given that f(x) = 2x² − 3x + 1, find f(−2).

  1. 3
  2. 15 Correct answer.
  3. −1
  4. 11

Explanation

Substitute x = −2 carefully: 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1. Squaring a negative gives a positive 4, and multiplying −3 by −2 gives +6. The total is 8 + 6 + 1 = 15.

Question 37Algebra and algebraic manipulation

Which of these is the correct simplification of (2x³y)(3xy⁴)?

  1. 6x⁴y⁴
  2. 5x⁴y⁵
  3. 6x³y⁴
  4. 6x⁴y⁵ Correct answer.

Explanation

Multiply the coefficients: 2 × 3 = 6. For the same base, add the indices: x³ × x¹ = x⁴ and y¹ × y⁴ = y⁵. The simplified product is therefore 6x⁴y⁵.

Question 38Algebra and algebraic manipulation

Solve the inequality 4 − 3x < 13.

  1. x < 3
  2. x < −3
  3. x > 3
  4. x > −3 Correct answer.

Explanation

Subtract 4 from both sides to get −3x < 9. Dividing both sides by −3 reverses the inequality sign, giving x > −3. Reversing the sign when dividing by a negative number is the key step.

Question 39Algebra and algebraic manipulation

Solve the simultaneous equations 2x + y = 11 and x − y = 1.

  1. x = 5, y = 1
  2. x = 4, y = 3 Correct answer.
  3. x = 3, y = 4
  4. x = 4, y = 5

Explanation

Adding the two equations eliminates y because y + (−y) = 0, giving 3x = 12, so x = 4. Substituting into x − y = 1 gives 4 − y = 1, so y = 3. Checking in 2x + y gives 8 + 3 = 11, which is correct.

Question 40Algebra and algebraic manipulation

Factorise x² − 5x − 24.

  1. (x − 6)(x + 4)
  2. (x + 8)(x − 3)
  3. (x − 12)(x + 2)
  4. (x − 8)(x + 3) Correct answer.

Explanation

We need two numbers whose product is −24 and whose sum is −5. The pair −8 and +3 works: −8 × 3 = −24 and −8 + 3 = −5. Hence x² − 5x − 24 = (x − 8)(x + 3).

Question 41Algebra and algebraic manipulation

A straight line passes through the points (2, 5) and (6, 13). What is the equation of the line?

  1. y = 2x + 5
  2. y = 2x + 1 Correct answer.
  3. y = 0.5x + 4
  4. y = 4x − 3

Explanation

The gradient is (13 − 5)/(6 − 2) = 8/4 = 2. Using y = mx + c with the point (2, 5): 5 = 2(2) + c, so c = 1. The equation is y = 2x + 1, and both points satisfy it.

Question 42Algebra and algebraic manipulation

Solve the quadratic equation x² − 7x + 10 = 0.

  1. x = 2 or x = −5
  2. x = −2 or x = −5
  3. x = 1 or x = 10
  4. x = 2 or x = 5 Correct answer.

Explanation

Factorising gives (x − 2)(x − 5) = 0, since −2 and −5 multiply to +10 and add to −7. Setting each factor to zero gives x = 2 or x = 5. Both values satisfy the original equation.

Question 43Algebra and algebraic manipulation

Simplify the algebraic fraction (x² − 9)/(x² + x − 12), stating any restriction on x.

  1. (x² − 9)/(x² + x − 12) cannot be simplified
  2. (x + 3)/(x + 4), x ≠ −4
  3. (x − 3)/(x + 4), x ≠ −4
  4. (x − 3)/(x − 4), x ≠ 4 Correct answer.

Explanation

Factorise both parts: the numerator is (x − 3)(x + 3) and the denominator is (x + 4)(x − 3). Cancelling the common factor (x − 3) leaves (x + 3)/(x + 4). The cancelled factor must not be zero, so x ≠ 3, and the denominator also requires x ≠ −4.

Question 44Algebra and algebraic manipulation

The quadratic expression x² + 8x + 5 is written in the form (x + p)² + q. What are the values of p and q?

  1. p = 4, q = −11 Correct answer.
  2. p = 8, q = −59
  3. p = −4, q = 21
  4. p = 4, q = 5

Explanation

Complete the square: x² + 8x + 5 = (x + 4)² − 16 + 5. Half of 8 is 4, and squaring 4 gives 16, which must be subtracted. Hence p = 4 and q = −11.

Question 45Algebra and algebraic manipulation

Given f(x) = x + 3 and g(x) = 2x − 1, find the composite function fg(x).

  1. 2x + 5
  2. 2x − 4
  3. 2x² + 5x − 3
  4. 2x + 2 Correct answer.

Explanation

The notation fg(x) means f(g(x)), so substitute g(x) into f. f(2x − 1) = (2x − 1) + 3 = 2x + 2. Applying f first would give a different result, so the order matters.

Question 46Algebra and algebraic manipulation

Solve the equation 3/(x − 2) = 5/(x + 1).

  1. x = 1.5
  2. x = 6.5 Correct answer.
  3. x = 2
  4. x = −6.5

Explanation

Cross-multiply to get 3(x + 1) = 5(x − 2), so 3x + 3 = 5x − 10. Rearranging gives 13 = 2x, so x = 6.5. Substituting back confirms both sides equal 3/4.5 and 5/7.5 respectively.

Question 47Algebra and algebraic manipulation

The sum of three consecutive odd integers is 57. What is the largest of the three integers?

  1. 19
  2. 21 Correct answer.
  3. 17
  4. 23

Explanation

Let the integers be n, n + 2 and n + 4, since consecutive odd numbers differ by 2. Their sum is 3n + 6 = 57, so 3n = 51 and n = 17. The largest integer is 17 + 4 = 21.

Question 48Algebra and algebraic manipulation

Simplify (2x⁻²y³)³, giving your answer with positive indices.

  1. 8x⁶y⁹
  2. 6y⁹/x⁶
  3. 8y⁶/x⁵
  4. 8y⁹/x⁶ Correct answer.

Explanation

Raise each factor to the power 3: 2³ = 8, (x⁻²)³ = x⁻⁶ and (y³)³ = y⁹. Writing x⁻⁶ with a positive index gives 1/x⁶, so the result is 8y⁹/x⁶.

Question 49Algebra and algebraic manipulation

Using the quadratic formula, solve 2x² − 4x − 3 = 0, giving your answers correct to 2 decimal places.

  1. x = 3.00 or x = −0.50
  2. x = 2.82 or x = −0.82
  3. x = 2.58 or x = −0.58 Correct answer.
  4. x = 1.58 or x = −1.58

Explanation

Here a = 2, b = −4 and c = −3, so the discriminant is b² − 4ac = 16 + 24 = 40. Then x = (4 ± √40)/4 = (4 ± 6.3246)/4, giving x ≈ 2.58 or x ≈ −0.58.

Question 50Algebra and algebraic manipulation

The expression x² + kx + 16 is a perfect square for a positive value of k. What is k?

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

Explanation

A perfect square of the form (x + a)² expands to x² + 2ax + a². Matching a² = 16 gives a = 4, so k = 2a = 8. The expression is then (x + 4)².