Finished: Math Practice Questions 4/05/2025

Here are 10 algebra practice questions for a New Zealand student preparing for NCEA Level 1:

Question 1

Solve for ( x ):
[ 3x + 7 = 16 ]

Steps:

3x = 9

x = 3

Answer: x = 3

Question 2

Expand and simplify:
[ 2(x + 4) - 3(x - 1) ]

Steps:

2x+8-3x+3

-x+11

Answer: -x+11

Question 3

Factorize 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

3y=6

y=2

Answer: y=2 and x=4

Question 5

Simplify:
{4x^2 - 8x}/{2x}

Steps:

2x(2x-4)/2x

x(2x-4)/x

2x-4

Answer: 2x-4

Question 6

Solve for ( x ):
5(2x - 3) = 4x + 7

Steps:

10x-15=4x+7

10x=4x+22

6x=22

x = 22/6

x = 11/3

Answer: x = 11/3

Question 7

Find the value of ( y ) when ( x = 2 ) in the equation:
[ y = 3x^2 - 5x + 1 ]

Steps:

y=3*2^2 -5*2+1

y=12-10+1

y=2+1

y=3

Answer: y=3

Question 8

Solve the simultaneous equations:
[ 3x + 2y = 12 ]
[ x - y = 1 ]

Steps:

based on equation 2

x=1+y

putting this into equation 1

3+3y+2y=12

3+ 5y+12

5y=9

y=1.8

Answer: y=1.8 and x =2.8

Question 9

Simplify:
{2x + 6}/{x^2 - 9}

Steps:

2(x+3)/(x² -3²)

2(x+3)/((x+3)(x-3))

2/(x-3)

Answer: 2/(x-3)

Question 10

Solve for ( x ):
{x}/{4} + 3 = 7

Steps:

x/4=4

x=16

Answer: x=16

These questions cover key algebra skills needed for NCEA Level 1, including solving equations, expanding, factorising, simplifying fractions, and simultaneous equations. Let me know if you'd like any adjustments! by deepseek-chat