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UAE TLS Mathematics Test study materials
UAE TLS Mathematics Test study resources

UAE TLS Mathematics Test practice questions

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Question 1Number and Operations

In the number 47,382, what is the value of the digit 7?

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

Explanation

The value of a digit depends on its place in the number. In 47,382 the digit 7 is in the thousands place, so its value is 7 × 1,000 = 7,000.

Question 2Number and Operations

Round 6,849 to the nearest hundred.

  1. 6,900
  2. 6,800 Correct answer.
  3. 6,850
  4. 7,000

Explanation

To round to the nearest hundred, look at the tens digit. The tens digit is 4, which is less than 5, so the hundreds digit stays 8 and the remaining digits become zero.

Question 3Number and Operations

Which of these numbers is a factor of 36?

  1. 7
  2. 5
  3. 8
  4. 9 Correct answer.

Explanation

A factor divides the number exactly with no remainder. Since 36 ÷ 9 = 4, the number 9 is a factor of 36.

Question 4Number and Operations

What is the lowest common multiple of 4 and 6?

  1. 12 Correct answer.
  2. 6
  3. 24
  4. 2

Explanation

List the multiples of each number: 4, 8, 12, 16, … and 6, 12, 18, …. The smallest number appearing in both lists is 12.

Question 5Number and Operations

Which fraction is equivalent to 3/5?

  1. 5/3
  2. 6/15
  3. 3/10
  4. 9/15 Correct answer.

Explanation

Multiplying the numerator and denominator of a fraction by the same nonzero number gives an equivalent fraction. Multiplying both parts of 3/5 by 3 gives 9/15.

Question 6Number and Operations

Write 0.75 as a fraction in its simplest form.

  1. 1/75
  2. 75/10
  3. 7/5
  4. 3/4 Correct answer.

Explanation

The decimal 0.75 means 75 hundredths, so it equals 75/100. Dividing the numerator and denominator by 25 gives 3/4.

Question 7Number and Operations

Calculate −5 + 8.

  1. 13
  2. −3
  3. 3 Correct answer.
  4. −13

Explanation

Starting at −5 on the number line and moving 8 places to the right gives 3. Equivalently, 8 − 5 = 3 and the result is positive because 8 is larger in size than 5.

Question 8Number and Operations

Evaluate 3 + 4 × 2.

  1. 9
  2. 24
  3. 14
  4. 11 Correct answer.

Explanation

Multiplication is performed before addition unless brackets show otherwise. First compute 4 × 2 = 8, then add 3 to get 11.

Question 9Number and Operations

What is 15% of 240?

  1. 24
  2. 160
  3. 3.6
  4. 36 Correct answer.

Explanation

To find a percentage of a quantity, write the percentage as a decimal and multiply. Here 0.15 × 240 = 36.

Question 10Number and Operations

A quantity of 84 is divided in the ratio 3 : 4. What is the smaller share?

  1. 48
  2. 36 Correct answer.
  3. 28
  4. 42

Explanation

The ratio has 3 + 4 = 7 equal parts. One part is 84 ÷ 7 = 12, so the shares are 3 × 12 = 36 and 4 × 12 = 48. The smaller share is 36.

Question 11Number and Operations

Calculate 2/3 + 1/4.

  1. 3/12
  2. 3/7
  3. 8/3
  4. 11/12 Correct answer.

Explanation

Rewrite the fractions with the common denominator 12: 2/3 = 8/12 and 1/4 = 3/12. Adding gives 8/12 + 3/12 = 11/12.

Question 12Number and Operations

Calculate 0.6 × 0.4.

  1. 0.024
  2. 2.4
  3. 0.24 Correct answer.
  4. 2.40

Explanation

Multiply 6 by 4 to get 24, then place the decimal point so that the answer has two decimal places, because 0.6 and 0.4 each have one. Thus 0.6 × 0.4 = 0.24.

Question 13Number and Operations

What is the highest common factor of 18 and 24?

  1. 12
  2. 6 Correct answer.
  3. 72
  4. 3

Explanation

The common factors of 18 and 24 are 1, 2, 3, and 6, and the largest of these is 6. Prime factorisation gives 18 = 2 × 3² and 24 = 2³ × 3, so the HCF is 2 × 3 = 6.

Question 14Number and Operations

Which expression shows 72 as a product of prime factors?

  1. 2⁴ × 3
  2. 2² × 3³
  3. 2 × 3⁴
  4. 2³ × 3² Correct answer.

Explanation

Divide 72 repeatedly by prime numbers: 72 = 8 × 9 = 2³ × 3². Every factor in this product is prime and their product is 72.

Question 15Number and Operations

Write 0.00045 in standard form.

  1. 4.5 × 10⁻³
  2. 45 × 10⁻⁵
  3. 4.5 × 10⁴
  4. 4.5 × 10⁻⁴ Correct answer.

Explanation

In standard form a number is written as a value between 1 and 10 multiplied by a power of 10. Moving the decimal point 4 places to the right gives 4.5, so the power is −4.

Question 16Number and Operations

What is the value of 2⁻³?

  1. 1/8 Correct answer.
  2. 8
  3. −8
  4. −6

Explanation

A negative exponent means take the reciprocal of the corresponding positive power. Therefore 2⁻³ = 1/2³ = 1/8.

Question 17Number and Operations

A price of 80 dirhams is increased by 15%. What is the new price?

  1. 95 dirhams
  2. 92 dirhams Correct answer.
  3. 68 dirhams
  4. 120 dirhams

Explanation

An increase of 15% means the new price is 115% of the old price. Thus 80 × 1.15 = 92 dirhams.

Question 18Number and Operations

Between which two consecutive integers does √50 lie?

  1. 8 and 9
  2. 6 and 7
  3. 7 and 8 Correct answer.
  4. 24 and 26

Explanation

Since 7² = 49 and 8² = 64, the square root of 50 is greater than 7 but less than 8. Therefore √50 lies between 7 and 8.

Question 19Number and Operations

A whole number is divisible by both 3 and 5. Which number must it also be divisible by?

  1. 30
  2. 45
  3. 8
  4. 15 Correct answer.

Explanation

Because 3 and 5 have no common factor other than 1, any number divisible by both must be divisible by their product, 3 × 5 = 15.

Question 20Number and Operations

Write 5/8 as a decimal.

  1. 0.625 Correct answer.
  2. 1.6
  3. 0.85
  4. 0.58

Explanation

Divide the numerator by the denominator: 5 ÷ 8 = 0.625. This is a terminating decimal because the denominator 8 = 2³ contains only the prime factor 2.

Question 21Number and Operations

Simplify (3⁴ × 3⁻²) ÷ 3³.

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

Explanation

When multiplying powers with the same base, add the exponents, and when dividing, subtract them. This gives 3^(4 + (−2) − 3) = 3⁻¹ = 1/3.

Question 22Number and Operations

Two numbers have highest common factor 6 and lowest common multiple 72. If one number is 18, what is the other number?

  1. 24 Correct answer.
  2. 48
  3. 12
  4. 36

Explanation

For two positive integers, the product of the numbers equals the product of their HCF and LCM. Thus the other number is (6 × 72) ÷ 18 = 432 ÷ 18 = 24.

Question 23Number and Operations

After a 20% discount, an item costs 64 dirhams. What was the original price?

  1. 84 dirhams
  2. 80 dirhams Correct answer.
  3. 128 dirhams
  4. 76.80 dirhams

Explanation

After a 20% discount, the customer pays 80% of the original price. If 80% of the original price is 64, then the original price is 64 ÷ 0.8 = 80 dirhams.

Question 24Number and Operations

Calculate (2.4 × 10⁵) ÷ (8 × 10²), giving the answer in standard form.

  1. 3 × 10³
  2. 3 × 10² Correct answer.
  3. 3 × 10⁴
  4. 0.3 × 10²

Explanation

Divide the numerical parts and subtract the exponents: 2.4 ÷ 8 = 0.3 and 10⁵ ÷ 10² = 10³. Thus the value is 0.3 × 10³ = 3 × 10².

Question 25Number and Operations

Which of these numbers is irrational?

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

Explanation

An irrational number cannot be written as a fraction of two integers. Since 7 is not a perfect square, √7 is irrational, while √16 = 4, 0.25 = 1/4, and 22/7 are all rational.

Question 26Number and Operations

Round 0.04726 to 2 significant figures.

  1. 0.047 Correct answer.
  2. 0.05
  3. 0.0473
  4. 0.048

Explanation

The first two significant figures are 4 and 7. The next digit is 2, which is less than 5, so the 7 is not rounded up. Therefore the value is 0.047.

Question 27Number and Operations

Calculate (−3) × (−4) ÷ (−2).

  1. −24
  2. −6 Correct answer.
  3. 6
  4. 24

Explanation

Multiply (−3) by (−4) to get 12 because the product of two negative numbers is positive. Then divide 12 by (−2), which gives −6 because a positive divided by a negative is negative.

Question 28Number and Operations

Express the recurring decimal 0.444... as a fraction in its simplest form.

  1. 2/5
  2. 4/9 Correct answer.
  3. 3/7
  4. 5/9

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 29Number and Operations

A bag contains 60 sweets. Three-fifths of the sweets are red. Of the remaining sweets, one-quarter are blue, and the rest are green. How many green sweets are there?

  1. 6
  2. 18 Correct answer.
  3. 24
  4. 36

Explanation

Three-fifths of 60 is 36 red sweets, leaving 24 sweets. One-quarter of 24 is 6 blue sweets, so the remaining 24 − 6 = 18 sweets are green.

Question 30Number and Operations

Simplify √72 + √18.

  1. 12√2
  2. 9√2 Correct answer.
  3. 6√2
  4. 15√2

Explanation

Write each surd with the largest square factor removed: √72 = √36 × √2 = 6√2, and √18 = √9 × √2 = 3√2. Adding like surds gives 6√2 + 3√2 = 9√2.

Question 31Algebra and Functions

Expand and simplify: 3(2x − 5) − 2(x − 4).

  1. 4x − 23
  2. 8x − 7
  3. 4x + 23
  4. 4x − 7 Correct answer.

Explanation

Multiply each bracket by its coefficient, taking care with the negative sign on the second bracket: 6x − 15 − 2x + 8. Then collect like terms: 6x − 2x = 4x and −15 + 8 = −7.

Question 32Algebra and Functions

Solve the equation 5x − 7 = 3x + 9.

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

Explanation

Subtract 3x from both sides to gather the unknown terms: 2x − 7 = 9. Then add 7 to both sides to get 2x = 16, and divide by the coefficient 2 to obtain x = 8.

Question 33Algebra and Functions

For the function f(x) = x² − 3x + 1, what is the value of f(−2)?

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

Explanation

Substitute x = −2 into every occurrence of x: (−2)² − 3(−2) + 1. Since (−2)² = 4 and −3(−2) = +6, the value is 4 + 6 + 1 = 11.

Question 34Algebra and Functions

A straight line passes through the points (1, 3) and (5, 11). What is the gradient of the line?

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

Explanation

Gradient is the change in y divided by the change in x between two points on the line. Here the change in y is 11 − 3 = 8 and the change in x is 5 − 1 = 4, so the gradient is 8 ÷ 4 = 2.

Question 35Algebra and Functions

Factorise fully: x² − 9.

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

Explanation

The expression is a difference of two squares, since x² − 9 = x² − 3². A difference of squares factorises as (a − b)(a + b), giving (x − 3)(x + 3).

Question 36Algebra and Functions

What is the largest set of real numbers for which f(x) = 1/(x − 4) is defined?

  1. All real x
  2. x ≥ 4
  3. x ≠ 4 Correct answer.
  4. x > 4

Explanation

A rational function is undefined only where its denominator equals zero. Solving x − 4 = 0 gives x = 4, so every other real number is allowed.

Question 37Algebra and Functions

Make x the subject of the formula y = 3x − 5.

  1. x = y/3 + 5
  2. x = (y + 5)/3 Correct answer.
  3. x = 3y + 15
  4. x = (y − 5)/3

Explanation

Add 5 to both sides to undo the subtraction: y + 5 = 3x. Then divide both sides by 3 to isolate x, giving x = (y + 5)/3.

Question 38Algebra and Functions

Simplify 2³ × 2⁻⁵.

  1. −4
  2. 1/4 Correct answer.
  3. 1/2
  4. 16

Explanation

When multiplying powers with the same base, add the indices: 3 + (−5) = −2. So the expression equals 2⁻², and a negative index means the reciprocal of the positive power, giving 1/4.

Question 39Algebra and Functions

Solve x² − 5x + 6 = 0.

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

Explanation

Look for two numbers that multiply to +6 and add to −5; these are −2 and −3. Factorising gives (x − 2)(x − 3) = 0, and by the zero product rule x = 2 or x = 3.

Question 40Algebra and Functions

Solve the simultaneous equations 2x + 3y = 12 and x − y = 1.

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

Explanation

Rearrange the second equation as x = y + 1 and substitute into the first: 2(y + 1) + 3y = 12. This simplifies to 5y = 10, so y = 2, and then x = 2 + 1 = 3. Checking: 2(3) + 3(2) = 12 and 3 − 2 = 1.

Question 41Algebra and Functions

The function f is defined by f(x) = 4x − 7. Find f⁻¹(x).

  1. (x − 7)/4
  2. (x + 7)/4 Correct answer.
  3. 1/(4x − 7)
  4. 4x + 7

Explanation

Write y = 4x − 7, then swap the roles of x and y to get x = 4y − 7. Solving for y: x + 7 = 4y, so y = (x + 7)/4.

Question 42Algebra and Functions

The functions are f(x) = x + 2 and g(x) = 3x. Find gf(x).

  1. 3x + 6 Correct answer.
  2. 3x² + 2
  3. 3x + 2
  4. x + 5

Explanation

The notation gf(x) means g applied to the output of f, so substitute f(x) into g. This gives g(x + 2) = 3(x + 2) = 3x + 6.

Question 43Algebra and Functions

Find the remainder when x³ − 2x² + 4 is divided by (x − 2).

  1. 12
  2. 8
  3. 0
  4. 4 Correct answer.

Explanation

By the remainder theorem, dividing a polynomial P(x) by (x − a) leaves remainder P(a). Here P(2) = 8 − 8 + 4 = 4.

Question 44Algebra and Functions

Given P(x) = x³ − 2x² − 5x + 6, which of these is a factor of P(x)?

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

Explanation

By the factor theorem, (x − a) is a factor exactly when P(a) = 0. Testing a = 3 gives 27 − 18 − 15 + 6 = 0, so (x − 3) is a factor.

Question 45Algebra and Functions

How many real roots does the equation x² − 4x + 7 = 0 have?

  1. Two distinct real roots
  2. Infinitely many real roots
  3. No real roots Correct answer.
  4. Exactly one repeated real root

Explanation

The number of real roots is determined by the discriminant b² − 4ac. Here b² − 4ac = 16 − 28 = −12, and a negative discriminant means there are no real roots.

Question 46Algebra and Functions

Express x² + 6x + 5 in the form (x + p)² + q.

  1. (x + 3)² − 4 Correct answer.
  2. (x + 3)² + 4
  3. (x − 3)² − 4
  4. (x + 6)² − 31

Explanation

Halve the coefficient of x to get p = 3, then subtract the square of that number. So x² + 6x + 5 = (x + 3)² − 9 + 5 = (x + 3)² − 4.

Question 47Algebra and Functions

Solve 2^(x + 1) = 32.

  1. x = 5
  2. x = 6
  3. x = 4 Correct answer.
  4. x = 16

Explanation

Write both sides as powers of 2: 32 = 2⁵, so 2^(x + 1) = 2⁵. Since the bases are equal, the indices must be equal, giving x + 1 = 5 and hence x = 4.

Question 48Algebra and Functions

Evaluate log₂8 + log₂4.

  1. 12
  2. 5 Correct answer.
  3. 7
  4. 32

Explanation

log₂8 asks for the power of 2 that gives 8, which is 3, and log₂4 = 2. Adding the values gives 3 + 2 = 5.

Question 49Algebra and Functions

Solve the inequality x² − x − 6 ≤ 0.

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

Explanation

Factorising gives (x − 3)(x + 2) ≤ 0, so the parabola crosses the x-axis at x = −2 and x = 3. The parabola opens upwards, so it is at or below zero between the roots: −2 ≤ x ≤ 3.

Question 50Algebra and Functions

The curve y = x² is transformed to give y = (x − 2)² + 3. Which translation describes the change?

  1. 2 units left and 3 units down
  2. 2 units right and 3 units up Correct answer.
  3. 2 units right and 3 units down
  4. 2 units left and 3 units up

Explanation

Replacing x with (x − 2) shifts the graph 2 units in the positive x direction, so it moves right. Adding 3 outside the bracket shifts the graph 3 units in the positive y direction, so it moves up.