Algebra Learning Quizzes for Year 11 Secondary School Students in the UK

Question 1

Which of the following is not a property of vectors?

Accepted Answer

Vectors can only be represented by arrows.

Answer

Vectors have both magnitude and direction.

Answer

Vectors can be added and subtracted.

Answer

Vectors can be multiplied by scalars.

Question 2

Draw the graph of the absolute value function f(x) = |x - 2|.

Accepted Answer

a. V-shaped graph with a vertex at (2, 0)

Answer

b. U-shaped graph with a vertex at (0, 2)

Answer

c. Straight line graph with a slope of 1 and a y-intercept of -2

Answer

d. Curved graph with a vertex at (0, 0)

Question 3

Which of the following statements represents an inequality?

Accepted Answer

x > 5

Answer

x = 5

Answer

x is less than 5

Answer

x + 5 = 10

Question 4

Solve the system of equations:
x + y = 5
x - y = 1

Accepted Answer

(2, 3)

Answer

(3, 2)

Answer

(1, 4)

Answer

(4, 1)

Question 5

Calculate the slope of the line that passes through the points (1, 2) and (3, 8).

Accepted Answer

3

Answer

2

Answer

4

Answer

6

Question 6

Which of the following is the graph of the function y = 2x - 3?

Accepted Answer

(Image of a line with a gradient of 2 and a y-intercept of -3.)

Answer

(Image of a line with a gradient of -2 and a y-intercept of 3.)

Answer

(Image of a parabola opening upwards.)

Answer

(Image of a circle.)

Question 7

Solve the inequality: x - 5 < 2

Accepted Answer

x < 7

Answer

x > 7

Answer

x < -7

Answer

x > -7

Question 8

Simplify the expression: (2x + 3)(x - 1)

Accepted Answer

2x^2 - x - 3

Answer

2x^2 + 5x - 3

Answer

4x^2 + 5x - 3

Answer

4x^2 - x - 3

Question 9

Expand and simplify the algebraic expression: (3x - 2)(x + 1)

Accepted Answer

3x^2 - 5x + 2

Answer

3x^2 + 5x - 2

Answer

3x^2 - x - 2

Answer

3x^2 + x - 2

Question 10

Translate the function f(x) = 2x + 3 two units to the left.

Accepted Answer

f(x) = 2(x - 2) + 3

Answer

f(x) = 2x + 1

Answer

f(x) = 2(x + 2) + 3

Answer

f(x) = 2x - 3

Question 11

Solve the linear inequality: 3x - 5 > 10

Accepted Answer

x > 5

Answer

x < 5

Answer

x > -5

Answer

x < -5

Question 12

Determine the gradient of the linear function y = 3x + 2.

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 13

Which of the following is not a type of function transformation?

Accepted Answer

Substitution

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 14

Solve the inequality: 2x - 5 > 11.

Accepted Answer

x > 8

Answer

x < 8

Answer

x > -8

Answer

x < -8

Question 15

Simplify the algebraic expression: 3x - 2y + 4x + 5y

Accepted Answer

7x + 3y

Answer

7x - 3y

Answer

5x + 7y

Answer

5x - 7y

Question 16

A farmer has 120 meters of fencing to enclose a rectangular plot of land. What dimensions of the plot will maximize its area?

Accepted Answer

40m x 80m

Answer

60m x 60m

Answer

50m x 70m

Answer

30m x 90m

Question 17

Find the gradient of the line passing through the points (2, 5) and (4, 9).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 18

Which of the following is the domain of the function: f(x) = sqrt(x - 2)?

Accepted Answer

[2, ∞)

Answer

[0, ∞)

Answer

(-∞, 2]

Answer

(0, 2)

Question 19

Which of the following is an arithmetic sequence?

Accepted Answer

2, 4, 6, 8, 10

Answer

1, 1, 2, 3, 5

Answer

2, 4, 8, 16, 32

Answer

1, 3, 6, 10, 15

Question 20

Which of the following transformations would shift the graph of the function y = f(x) 2 units to the left?

Accepted Answer

g(x) = f(x - 2)

Answer

g(x) = f(x + 2)

Answer

g(x) = f(2x)

Answer

g(x) = f(x)/2

Question 21

Solve the linear equation: 2x - 5 = 7

Accepted Answer

x = 6

Answer

x = 8

Answer

x = 7

Answer

x = 5

Question 22

What is the inverse function of f(x) = 2x + 1?

Accepted Answer

f^-1(x) = (x - 1) / 2

Answer

f^-1(x) = x / 2 + 1

Answer

f^-1(x) = 2x - 1

Answer

f^-1(x) = 1 - 2x

Question 23

Simplify the expression: (2x + 3)(x - 5)

Accepted Answer

2x^2 - 7x - 15

Answer

2x^2 - 15

Answer

2x^2 + 15

Answer

2x^2 + 7x - 15

Question 24

Factorise the expression: x^2 - 25

Accepted Answer

(x + 5)(x - 5)

Answer

Cannot be factorised

Answer

(x + 5)^2

Answer

(x - 5)^2

Question 25

What is the gradient of the line with the equation y = 2x + 3?

Accepted Answer

2

Answer

3

Answer

-2

Answer

1

Question 26

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 5x + 6 = 0

Answer

2x - 3y = 4

Answer

√(x) = 2

Answer

x + 5 = 10

Question 27

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Answer

(x + 9)(x - 9)

Question 28

The graph of the function f(x) = x^2 - 4x + 3 is a parabola that:

Accepted Answer

Opens upwards and has its vertex at (2, -1)

Answer

Opens downwards and has its vertex at (2, -1)

Answer

Opens upwards and has its vertex at (-2, 1)

Answer

Opens downwards and has its vertex at (-2, 1)

Question 29

Solve the following equation: 2(x - 3) + 5 = 15

Accepted Answer

x = 8

Answer

x = 5

Answer

x = 10

Answer

x = 6

Question 30

Factorize the following expression: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

x(x - 4)

Answer

(x + 4)(x - 4)

Question 31

Which of the following is a quadratic function?

Accepted Answer

f(x) = x^2 + 2x + 1

Answer

f(x) = x^3 + 2

Answer

f(x) = sqrt(x)

Answer

f(x) = ln(x)

Question 32

What is the gradient of the line that passes through the points (2, 3) and (5, 7)?

Accepted Answer

1

Answer

2

Answer

1/2

Answer

-1

Question 33

What is the inverse operation of squaring a number?

Accepted Answer

Square rooting

Answer

Multiplying

Answer

Adding

Answer

Dividing

Question 34

What is the domain of the function f(x) = 1 / (x - 2)?

Accepted Answer

All real numbers except x = 2

Answer

x < 2

Answer

x > 2

Answer

All real numbers

Question 35

Find the coordinates of the vertex of the parabola y = x^2 - 4x + 3.

Accepted Answer

(2, -1)

Answer

(-2, 1)

Answer

(0, 3)

Answer

(4, -1)

Question 36

Which of the following is the graph of the linear function y = 2x + 1?

Accepted Answer

(Image of a straight line passing through points (0, 1) and (1, 3))

Answer

(Image of a circle)

Answer

(Image of a parabola opening upwards)

Question 37

Solve the inequality: 3x - 2 > 10

Accepted Answer

x > 4

Answer

x > 2

Answer

x < 2

Answer

x < 4

Question 38

Find the domain of the rational function f(x) = 1/(x-2)

Accepted Answer

All real numbers except x = 2

Answer

x < 2

Answer

x > 2

Answer

All real numbers

Question 39

Solve the equation 3x + 5 = 14.

Accepted Answer

x = 3

Answer

x = 6

Answer

x = -3

Answer

x = 1

Question 40

What is the simplified form of the expression 2(x + 3) - 4x?

Accepted Answer

-2x + 6

Answer

6x + 6

Answer

2x + 6

Answer

-2x - 6

Question 41

A train travels at a speed of 60 miles per hour.  If it travels for 't' hours, what is the distance it covers?

Accepted Answer

60t miles

Answer

60/t miles

Answer

60 + t miles

Answer

t/60 miles

Question 42

The nth term of a sequence is given by the formula 2n + 1. What is the 5th term of this sequence?

Accepted Answer

11

Answer

9

Answer

10

Answer

12

Question 43

Solve the inequality 2x - 3 > 7.

Accepted Answer

x > 5

Answer

x > -5

Answer

x < 5

Question 44

Which of the following points lies on the line represented by the equation y = 2x - 1?

Accepted Answer

(2, 3)

Answer

(0, 1)

Answer

(3, 5)

Answer

(1, 1)

Question 45

The equation of a line is y = 3x + 2. What is the gradient of this line?

Accepted Answer

3

Answer

2

Answer

-2

Answer

-3

Question 46

What is the equation of the line passing through the points (1, 2) and (3, 6)?

Accepted Answer

y = 2x

Answer

y = -2x + 4

Answer

y = x + 1

Answer

y = 3x - 1

Question 47

The function f(x) = 2x - 1. What is the value of f(4)?

Accepted Answer

7

Answer

9

Answer

3

Answer

5

Question 48

The graph of the function y = x² is transformed by a translation 2 units to the right. What is the equation of the transformed graph?

Accepted Answer

y = (x - 2)²

Answer

y = x² - 2

Answer

y = x² + 2

Answer

y = (x + 2)²

Question 49

Solve for x: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = 1

Answer

x = -3

Answer

x = 6

Question 50

What is the simplified form of the expression 2(x + 3) - 4x?

Accepted Answer

-2x + 6

Answer

-2x - 6

Answer

6x + 6

Answer

2x + 6

Question 51

Which of the following is the solution to the inequality 2x - 1 > 5?

Accepted Answer

x > 3

Answer

x ≤ 3

Answer

x ≥ 3

Answer

x < 3

Question 52

The nth term of a sequence is given by the formula Tn = 3n - 2. What is the value of the 5th term?

Accepted Answer

13

Answer

8

Answer

10

Answer

15

Question 53

Which of the following is a function?

Accepted Answer

{(1, 2), (2, 4), (3, 6)}

Answer

{(1, 2), (2, 3), (3, 3)}

Answer

{(1, 2), (2, 2), (3, 2)}

Answer

{(1, 2), (2, 3), (1, 4)}

Question 54

What is the gradient of the line represented by the equation y = 2x + 3?

Accepted Answer

2

Answer

-2

Answer

3

Answer

-3

Question 55

The graph of y = x² is translated 3 units to the right. What is the equation of the translated graph?

Accepted Answer

y = (x - 3)²

Answer

y = (x + 3)²

Answer

y = x² + 3

Answer

y = x² - 3

Question 56

A car travels 120 miles in 2 hours. What is its average speed?

Accepted Answer

60 miles per hour

Answer

120 miles per hour

Answer

240 miles per hour

Answer

30 miles per hour

Question 57

Expand and simplify the expression (x + 2)(x - 3).

Accepted Answer

x² - x - 6

Answer

x² - 5x - 6

Answer

x² + x - 6

Answer

x² + 5x - 6

Question 58

The sum of two numbers is 20 and their difference is 4. What are the two numbers?

Accepted Answer

12 and 8

Answer

15 and 5

Answer

10 and 10

Answer

16 and 4