Finished: Math Practice Questions 4/05/2025

Here are 10 algebra practice questions for a NCEA Level 1 student, formatted with blank "Steps:" and "Answer:" sections for each question:

Question 1

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

Steps:

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 on equation 2

x=2+y

putting this into equation 1

4+2y+y=10

4+3y=10

3y=6

y=2

Answer: y=2 and x=4

Question 5

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

Steps: 2(2x² -8)/(2x-4)

2(2x² -8)/2(x-2)

2*2(x² -8)/2(x-2)

2(x² -8)/(x-2)

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

2(x+2)

2x+4

Answer: 2x+4

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 )
( x + y = 5 )

Steps:

based on equation 2

x=5-y

putting this into equation 1

15-3y+2y=12

15-y=12

-y=-3

y=3

Answer: y=3 and x =2

Question 9

Simplify:
(2x^3)^2 * x^{-4}

Steps:

2x³ * 2x³ * x^-4

4x^6 * x^-4

4x^6 / x^4

4x^2

Answer: 4x^2

Question 10

Solve for ( x ):
( x^2 - 5x + 6 = 0 )

Steps:

x * x -5 x + 6 = 0

(x-3) (x-2) = 0

Answer: x = 2 or 3

Let me know if you'd like any adjustments or additional questions! by deepseek-chat