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BGCSE Scientific Mathematics 1237 study materials
BGCSE Scientific Mathematics 1237 study resources

BGCSE Scientific Mathematics 1237 practice questions

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Question 1Number and Numeration

What is the value of the digit 7 in the number 4,782?

  1. 7,000
  2. 70
  3. 700 Correct answer.
  4. 7

Explanation

In a base-ten numeral each position is worth ten times the position on its right. The digit 7 sits in the hundreds place, so its value is 7 × 100 = 700.

Question 2Number and Numeration

Which of these numbers is a prime number?

  1. 39
  2. 33
  3. 29 Correct answer.
  4. 21

Explanation

A prime has exactly two factors, 1 and itself. 29 is not divisible by 2, 3, or 5 and has no factor below 6, so it is prime.

Question 3Number and Numeration

Write 0.375 as a fraction in its simplest form.

  1. 3/4
  2. 375/100
  3. 3/8 Correct answer.
  4. 1/3

Explanation

0.375 means 375/1000. Dividing numerator and denominator by 125 gives 3/8, and 3 and 8 share no common factor.

Question 4Number and Numeration

Round 6.847 to two decimal places.

  1. 6.84
  2. 6.8
  3. 6.85 Correct answer.
  4. 6.9

Explanation

Look at the third decimal digit, which is 7. Since 7 is 5 or more, the second decimal digit 4 is increased to 5, giving 6.85.

Question 5Number and Numeration

What is the highest common factor of 36 and 48?

  1. 144
  2. 12 Correct answer.
  3. 6
  4. 4

Explanation

Write 36 = 2² × 3² and 48 = 2⁴ × 3. The HCF takes the lower power of each shared prime: 2² × 3 = 12.

Question 6Number and Numeration

Which list is written in ascending order?

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

Explanation

On a number line, values increase from left to right, and negative numbers with larger digits are smaller. So −5 < −2 < 0 < 3.

Question 7Number and Numeration

Evaluate 2³ × 2², leaving the answer as a power of 2.

  1. 2⁵ Correct answer.
  2. 4⁵
  3. 2¹
  4. 2⁶

Explanation

When multiplying powers with the same base, add the indices: 3 + 2 = 5, so the product is 2⁵.

Question 8Number and Numeration

A shirt costs 40 pula and is reduced by 15%. What is the new price?

  1. 34 pula Correct answer.
  2. 46 pula
  3. 6 pula
  4. 25 pula

Explanation

The reduction is 15% of 40 = 0.15 × 40 = 6 pula. Subtracting the discount from the original price gives 40 − 6 = 34 pula.

Question 9Number and Numeration

Express 0.000 42 in standard form.

  1. 4.2 × 10⁴
  2. 4.2 × 10⁻⁴ Correct answer.
  3. 4.2 × 10⁻³
  4. 42 × 10⁻⁵

Explanation

Standard form writes a number as a × 10ⁿ with 1 ≤ a < 10. Moving the decimal point 4 places right gives 4.2, so the index is −4.

Question 10Number and Numeration

Convert the recurring decimal 0.444... to a fraction in simplest form.

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

Explanation

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

Question 11Number and Numeration

A recipe uses flour and sugar in the ratio 5 : 2. If 350 g of flour is used, how much sugar is needed?

  1. 70 g
  2. 245 g
  3. 175 g
  4. 140 g Correct answer.

Explanation

Each ratio part is worth 350 ÷ 5 = 70 g. Sugar is 2 parts, so the mass is 2 × 70 = 140 g.

Question 12Number and Numeration

Simplify 3√2 + 5√2 − √2.

  1. 8√2
  2. 15√2
  3. 7√6
  4. 7√2 Correct answer.

Explanation

Surds with the same radicand behave like algebraic terms, so add the coefficients: 3 + 5 − 1 = 7. The result is 7√2.

Question 13Number and Numeration

The number 2520 is written as a product of prime factors. What is the index of 2 in that product?

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

Explanation

Repeated division by 2 gives 2520 = 2 × 1260 = 2² × 630 = 2³ × 315, and 315 is odd. So the index of 2 is 3.

Question 14Number and Numeration

Evaluate (2/3) ÷ (4/9), giving the answer in simplest form.

  1. 8/27
  2. 3/2 Correct answer.
  3. 2/3
  4. 27/8

Explanation

Dividing by a fraction means multiplying by its reciprocal: 2/3 × 9/4 = 18/12 = 3/2.

Question 15Number and Numeration

Which of these numbers is irrational?

  1. √7 Correct answer.
  2. √16
  3. 0.25
  4. 22/7

Explanation

An irrational number cannot be written as a fraction of integers. Since 7 is not a perfect square, √7 has a non-terminating, non-recurring decimal expansion.

Question 16Number and Numeration

A car travels 150 km in 2 hours 30 minutes. What is its average speed in km/h?

  1. 50 km/h
  2. 62.5 km/h
  3. 60 km/h Correct answer.
  4. 75 km/h

Explanation

Convert the time to hours: 2 hours 30 minutes = 2.5 h. Average speed = distance ÷ time = 150 ÷ 2.5 = 60 km/h.

Question 17Number and Numeration

The mass of a sample is 0.003 06 kg. Written in standard form, this is

  1. 3.06 × 10⁻² kg
  2. 3.06 × 10⁻³ kg Correct answer.
  3. 3.06 × 10³ kg
  4. 30.6 × 10⁻⁴ kg

Explanation

In standard form the first factor must lie between 1 and 10. Moving the point 3 places right gives 3.06, so the index is −3.

Question 18Number and Numeration

What is the lowest common multiple of 12 and 18?

  1. 6
  2. 72
  3. 216
  4. 36 Correct answer.

Explanation

Write 12 = 2² × 3 and 18 = 2 × 3². The LCM takes the highest power of each prime: 2² × 3² = 36.

Question 19Number and Numeration

Evaluate 5⁰ + 5⁻¹, giving the answer as a decimal.

  1. 0.2
  2. 2.0
  3. 1.5
  4. 1.2 Correct answer.

Explanation

Any non-zero number to the power 0 equals 1, and 5⁻¹ = 1/5 = 0.2. Adding gives 1 + 0.2 = 1.2.

Question 20Number and Numeration

A sum of 800 pula is invested at 5% simple interest per year. What is the total amount after 3 years?

  1. 920 pula Correct answer.
  2. 840 pula
  3. 120 pula
  4. 926 pula

Explanation

Simple interest is P × R × T ÷ 100 = 800 × 5 × 3 ÷ 100 = 120 pula. The total amount is the principal plus interest: 800 + 120 = 920 pula.

Question 21Number and Numeration

A number N is written as 2⁴ × 3² × 5. How many positive factors does N have?

  1. 11
  2. 24
  3. 15
  4. 30 Correct answer.

Explanation

If N = pᵃ × qᵇ × rᶜ, the number of factors is (a+1)(b+1)(c+1). Here this is (4+1)(2+1)(1+1) = 5 × 3 × 2 = 30.

Question 22Number and Numeration

Simplify (2√3 + √5)(2√3 − √5).

  1. 12 + 4√15
  2. 12 − √15
  3. 17
  4. 7 Correct answer.

Explanation

This is a difference of two squares: (a + b)(a − b) = a² − b². Here a² = (2√3)² = 12 and b² = (√5)² = 5, so the result is 12 − 5 = 7.

Question 23Number and Numeration

Express 0.1 36 recurring (where 36 repeats) as a fraction in simplest form.

  1. 68/500
  2. 1/8
  3. 136/1000
  4. 3/22 Correct answer.

Explanation

Let x = 0.13636..., then 100x = 13.636... and x = 0.136.... Subtracting gives 99x = 13.5, so x = 13.5/99 = 27/198 = 3/22.

Question 24Number and Numeration

The mass of a grain of sand is about 2.5 × 10⁻⁵ kg. Approximately how many grains are in 1 kg of sand?

  1. 4 × 10⁻⁵
  2. 2.5 × 10⁵
  3. 4 × 10⁴ Correct answer.
  4. 4 × 10⁵

Explanation

Divide 1 by 2.5 × 10⁻⁵: 1 ÷ 2.5 = 0.4 and 0.4 ÷ 10⁻⁵ = 0.4 × 10⁵ = 4 × 10⁴ grains.

Question 25Number and Numeration

A quantity is increased by 20% and the result is then decreased by 20%. Compared with the original quantity, the final value is

  1. the same
  2. 4% less Correct answer.
  3. 20% less
  4. 4% more

Explanation

Multiplying by 1.2 then by 0.8 gives an overall factor of 0.96. So the final value is 96% of the original, which is a 4% decrease.

Question 26Number and Numeration

Write the number 3 400 000 in standard form.

  1. 0.34 × 10⁷
  2. 34 × 10⁵
  3. 3.4 × 10⁵
  4. 3.4 × 10⁶ Correct answer.

Explanation

Standard form writes a number as A × 10ⁿ where A lies between 1 and 10. Moving the decimal point 6 places left in 3 400 000 gives 3.4, so the value is 3.4 × 10⁶.

Question 27Number and Numeration

A bag contains red and blue beads in the ratio 3 : 5. If there are 24 red beads, how many blue beads are there?

  1. 64
  2. 40 Correct answer.
  3. 45
  4. 15

Explanation

The ratio 3 : 5 means each part of the ratio corresponds to 24 ÷ 3 = 8 beads. The blue beads make 5 parts, so there are 5 × 8 = 40 blue beads.

Question 28Number and Numeration

A trader buys a radio for 250 pula and sells it for 300 pula. What is the percentage profit?

  1. 25%
  2. 50%
  3. 16.7%
  4. 20% Correct answer.

Explanation

Profit is 300 − 250 = 50 pula, and percentage profit is always calculated on the cost price. So the profit percentage is (50 ÷ 250) × 100% = 20%.

Question 29Number and Numeration

The number 180 is written as a product of its prime factors. What is the index of 3 in that product?

  1. 1
  2. 3
  3. 2 Correct answer.
  4. 0

Explanation

Dividing 180 repeatedly by primes gives 180 = 2 × 90 = 2 × 2 × 45 = 2² × 3 × 3 × 5, so 180 = 2² × 3² × 5. The factor 3 appears twice, so its index is 2.

Question 30Number and Numeration

A school buys 240 exercise books and shares them among three classes in the ratio 2 : 3 : 5. How many books does the class with the largest share receive?

  1. 72
  2. 24
  3. 120 Correct answer.
  4. 48

Explanation

The ratio parts add to 2 + 3 + 5 = 10, so one part equals 240 ÷ 10 = 24 books. The largest share is 5 parts, giving 5 × 24 = 120 books. Checking: 48 + 72 + 120 = 240, which matches the total.

Question 31Algebra and Algebraic Processes

Simplify the expression 5x + 3y - 2x + 4y.

  1. 3x + 7y Correct answer.
  2. 3x + y
  3. 7x + 7y
  4. 7x - y

Explanation

Like terms are combined by adding their coefficients: 5x - 2x gives 3x, and 3y + 4y gives 7y. Terms with different letters cannot be merged into one term.

Question 32Algebra and Algebraic Processes

Expand and simplify 4(2a - 3) + 5.

  1. 8a - 7 Correct answer.
  2. 8a + 17
  3. 8a + 2
  4. 8a - 17

Explanation

Multiply each term inside the bracket by 4 to get 8a - 12, then add 5. Combining -12 and 5 gives -7, so the result is 8a - 7.

Question 33Algebra and Algebraic Processes

Solve the equation 3x - 7 = 14.

  1. x = 3
  2. x = 21
  3. x = 2
  4. x = 7 Correct answer.

Explanation

Add 7 to both sides to obtain 3x = 21, then divide both sides by 3. This gives x = 7, which checks back correctly in the original equation.

Question 34Algebra and Algebraic Processes

What is the value of 2x² + 3x when x = 4?

  1. 28
  2. 56
  3. 44 Correct answer.
  4. 20

Explanation

Substitute x = 4: 2(4²) + 3(4). Since 4² = 16, the expression becomes 32 + 12, which equals 44.

Question 35Algebra and Algebraic Processes

Which expression represents the statement 'seven less than three times a number n'?

  1. 7n - 3
  2. 3(n - 7)
  3. 7 - 3n
  4. 3n - 7 Correct answer.

Explanation

'Three times a number' is 3n, and 'seven less than' that quantity means subtracting 7 from it. The order matters, so the result is 3n - 7.

Question 36Algebra and Algebraic Processes

Factorise the expression 6x + 9.

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

Explanation

The highest common factor of 6x and 9 is 3. Dividing each term by 3 gives 2x and 3, so the factorised form is 3(2x + 3).

Question 37Algebra and Algebraic Processes

Solve the inequality x + 5 < 2.

  1. x < -3 Correct answer.
  2. x > 7
  3. x > -3
  4. x < 7

Explanation

Subtract 5 from both sides of the inequality. This gives x < 2 - 5, which simplifies to x < -3, and the inequality sign is unchanged because no negative multiplication occurred.

Question 38Algebra and Algebraic Processes

What is the gradient of the straight line passing through the points (1, 2) and (4, 11)?

  1. 9
  2. 3 Correct answer.
  3. 1/3
  4. 6

Explanation

Gradient equals the change in y divided by the change in x. Here that is (11 - 2)/(4 - 1) = 9/3 = 3.

Question 39Algebra and Algebraic Processes

Expand the product (x + 4)(x - 3).

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

Explanation

Multiply each term in the first bracket by each term in the second: x² - 3x + 4x - 12. Combining -3x and 4x gives x, so the result is x² + x - 12.

Question 40Algebra and Algebraic Processes

Factorise x² - 5x + 6.

  1. (x - 1)(x - 6)
  2. (x + 1)(x + 6)
  3. (x + 2)(x + 3)
  4. (x - 2)(x - 3) Correct answer.

Explanation

Two numbers must multiply to +6 and add to -5; these are -2 and -3. The factorised form is therefore (x - 2)(x - 3).

Question 41Algebra and Algebraic Processes

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

  1. x = 3, y = 4
  2. x = 5, y = 1
  3. x = 2, y = 7
  4. x = 4, y = 3 Correct answer.

Explanation

Adding the two equations eliminates y, giving 3x = 12, so x = 4. Substituting into x - y = 1 gives y = 3, and both equations are satisfied.

Question 42Algebra and Algebraic Processes

Make r the subject of the formula A = πr².

  1. r = √(Aπ)
  2. r = A/(2π)
  3. r = A/π²
  4. r = √(A/π) Correct answer.

Explanation

Divide both sides by π to obtain r² = A/π, then take the positive square root since r represents a length. This gives r = √(A/π).

Question 43Algebra and Algebraic Processes

Given f(x) = 3x - 2, what is the value of f⁻¹(7)?

  1. 7
  2. 3 Correct answer.
  3. 19
  4. 1/3

Explanation

Set 3x - 2 = 7 and solve: 3x = 9, so x = 3. This is the input that produces an output of 7 under f.

Question 44Algebra and Algebraic Processes

Simplify (2x³y²)(4x²y⁵).

  1. 6x⁵y⁷
  2. 8x⁵y¹⁰
  3. 8x⁵y⁷ Correct answer.
  4. 8x⁶y¹⁰

Explanation

Multiply the coefficients to get 8, then add the exponents of like bases. For x, 3 + 2 = 5; for y, 2 + 5 = 7, giving 8x⁵y⁷.

Question 45Algebra and Algebraic Processes

Solve the quadratic equation x² - 4x - 12 = 0.

  1. x = 6 or x = -2 Correct answer.
  2. x = 4 or x = -3
  3. x = 3 or x = -4
  4. x = -6 or x = 2

Explanation

The expression factorises as (x - 6)(x + 2), since -6 and 2 multiply to -12 and add to -4. Setting each factor to zero gives x = 6 or x = -2.

Question 46Algebra and Algebraic Processes

A straight line has equation 3x + 2y = 12. What is its gradient?

  1. -3/2 Correct answer.
  2. -2/3
  3. 3/2
  4. 2/3

Explanation

Rearrange into the form y = mx + c: 2y = -3x + 12, so y = -1.5x + 6. The coefficient of x, which is -3/2, is the gradient.

Question 47Algebra and Algebraic Processes

The sum of three consecutive integers is 87. What is the largest of the three integers?

  1. 30 Correct answer.
  2. 31
  3. 28
  4. 29

Explanation

Let the integers be n, n + 1 and n + 2. Their sum is 3n + 3 = 87, so 3n = 84 and n = 28. The largest integer is therefore 30.

Question 48Algebra and Algebraic Processes

Simplify the algebraic fraction (x² - 9)/(x + 3), stating any restriction.

  1. x² - 3, provided x ≠ 0
  2. x - 3, provided x ≠ 3
  3. x - 3, provided x ≠ -3 Correct answer.
  4. x + 3, provided x ≠ 3

Explanation

The numerator factorises as (x - 3)(x + 3). Cancelling the common factor (x + 3) leaves x - 3, but the original denominator is zero when x = -3, so that value must be excluded.

Question 49Algebra and Algebraic Processes

Solve the equation 5/(x - 2) = 3 for x.

  1. x = 17/3
  2. x = 11/3 Correct answer.
  3. x = 13/3
  4. x = 3/5

Explanation

Multiply both sides by (x - 2) to get 5 = 3(x - 2), so 5 = 3x - 6. Adding 6 gives 3x = 11 and hence x = 11/3, which is valid since x ≠ 2.

Question 50Algebra and Algebraic Processes

The quadratic expression x² + kx + 9 is a perfect square for a positive value of k. What is k?

  1. 6 Correct answer.
  2. 18
  3. 3
  4. 9

Explanation

A perfect square has the form (x + a)² = x² + 2ax + a². Matching a² = 9 gives a = 3, so k = 2a = 6, and the expression equals (x + 3)².