Finished: Math Practice Questions 7/05/2025

Here are 10 algebra practice questions for NCEA Level 1, formatted as requested:

Question 1

Solve for ( x ):
( 3x + 7 = 22 )

Steps:

move 7 over

3x = 15

x=5

Answer: x=5

Question 2

Expand and simplify:
( 2(x + 5) - 3(x - 2) )

Steps:

2x+10-3x+6

-x+16

Answer: -x+16

Question 3

Factorise fully:
( 6x^2 - 9x )

Steps:

3x(2x-3)

Answer: 3x(2x-3)

Question 4

Solve the simultaneous equations:
( 2x + y = 10 )
( x - y = 2 )

Steps:

based one equation 2

x=2+y

putting this into equation 1

4+2y+y=10

3y=6

y=2

Answer: y=2 and x =4

Question 5

Simplify the expression:
{4x^2 - 16}/{2x - 4} )

Steps:

2(2x^2-8)/2x-4

2(2x^2-8)/2(x-2)

2*2 (x^2-4)/2(x-2)

2 (x^2-4)/(x-2)

2(x-2) * (x+2) /x-2

2(x+2)

Answer: 2(x+2)

Question 6

Solve for ( x )

{3x}{5} = 9

Steps:

3x=45

x=15

Answer: x=15

Question 7

Solve the inequality:
( 5 - 2x \leq 11 )

Steps:

-2x \leq 6

-x \leq 3

x\geq -3

Answer: x\geq -3

Question 8

Solve the simultaneous equations:
( 3x + 2y = 12 )
( 4x - y = 5 )

Steps:

based on equation 2

-y=5-4x=5

y=-5+4x=5

putting this into equation 1

3x -10+8x=12

11x=22

x=2

Answer: x=2 and y =3

Question 9

A rectangle has a length of ( (2x + 3) ) cm and a width of ( (x - 1) ) cm. Write an expression for its area in expanded form.

Steps:

(2x + 3) *(x - 1)

2x^2-2x+3x-3

Answer: 2x^2-2x+3x-3

Question 10

(18 / (6 - 3)) + 5 × 2^2

simplify

Steps:

18/3+5 *4

6+5*4

6+20

26

Answer: 26

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