Algebra 1

Question 1

What is an equation?

Answer 1

An expression that has an ‘=’ sign in it

Question 2

True or False?
(2x + 3)² = 4x² + 9

Answer 2

False
(2x + 3)²
= (2x + 3)(2x + 3)
= 4x² + 6x + 6x + 9
= 4x² + 12x + 9

Question 3

What is the first step to solve equations that involve brackets?

Answer 3

Expand the bracket

Question 4

What is the first thing you would do to rearrange
x = 2y - 5
to make y the subject?

Answer 4

Add 5 to both sides

Question 5

What is a term?

Answer 5

A single or group of numbers/letters together.
(not added or subtracted)
e.g. 5, y, 3x, 4ab²

Question 6

What is the first step to make an expression from a worded problem?

Answer 6

Work out what the variable is

Question 7

Expand 3(2x - 5)

Answer 7

6x - 15

Question 8

What goes outside the bracket when factorising an expression?

Answer 8

The highest common factors of all the terms in the original expression.

Question 9

A function machine takes a number,
divides it by 3,
then adds 4.
What is the output when 9 is put into the machine?

Answer 9

7

Question 10

What is the first step to collect like terms?

Answer 10

Identify the terms that are the same type as each other

Question 11

How do you expand a single bracket?

Answer 11

Multiply each term inside the bracket by the bit outside the bracket

Question 12

What is
a x a x b x b
in its simplest form?

Answer 12

a²b²
Or
(ab)²

Question 13

What is a formula?

Answer 13

A rule that helps you work something out
(has an ‘=’ sign)

Question 14

Expand and simplify
(x + 3)(x - 1)

Answer 14

(x + 3)(x - 1)
= x² - x + 3x - 3
= x² + 2x - 3

Question 15

Harry is three years older than Max.
Shelly is twice as old as Max.
Give an expression for the sum of their ages.

Answer 15

Let Max’s age be x
Then Harry is x + 3
and Shelly is 2x

Sum of their ages = x + x + 3 + 2x = 4x + 3

Question 16

True of False?
When rearranging a formula,
you should do the opposite thing to each side.

Answer 16

False
You should do the same thing to both sides

Question 17

How do you find the value put into a function machine, from the output?

Answer 17

Use the function machine in reverse.
Starting with the output value,
and doing the inverse operation at each stage

Question 18

How could you check that a factorisation is correct?

Answer 18

Multiply it out again and check you get the original expression

Question 19

Solve
x + 8 = 5

Answer 19

x = -3

Question 20

What is the rule for factorising the difference between two squares?

Answer 20

Square root the first term and put this at the start of each bracket.

Square root the second term and put this at the back of each bracket.

One bracket has a plus, the other a minus

Question 21

What is an expression?

Answer 21

A collection of terms without an ‘=’ sign

Question 22

Simplify
2y + 9 - 6y - 4

Answer 22

-4y + 5

Question 23

What is the first thing you should do to expand squared brackets?

Answer 23

Write them out as double brackets

Question 24

1 km = 1.6m
What is 10 miles in kilometres?

Answer 24

16 km

Question 25

What is the first thing you'd do to solve 5x - 9 = 6

Answer 25

Add 9 to both sides

Question 26

How would you write 8 lots of a multiplied together? a x a x a x a x a x a x a x a

Answer 26

a⁸

Question 27

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

Answer 27

x(4x - 1) - 3x(2x + 3) = 4x² - x - 6x² - 9x = -2x² - 10x

Question 28

Make b the subject a = ½( 5b - 3)

Answer 28

a = ½( 5b - 3) (x2) 2a = 5b - 3 (+3) 2a + 3 = 5b (÷5) 2a + 3 = b 5

Question 28

Factorise x² - 49

Answer 28

Difference between two squares (x + 7)(x-7)

Question 29

A function machine takes a number, multiplies it by 5, then subtracts 3. What is the input if the output is 17 ?

Answer 29

17 + 3 = 20 20 ÷ 5 = 4 4

Question 30

Simplify 3 x p x p x q

Answer 30

3p²q

Question 31

What is meant by factorising an expression?

Answer 31

Putting brackets into the expression

Question 32

What is the first step to solve equations that have an x on both sides?

Answer 32

Get all the x terms on one side of the equation by getting rid of the lowest value of x from both sides. Then get all the numbers on the other side of the equation

Question 33

Factorise fully 4x² + 6xy + 12xy²

Answer 33

2x(2x + 3y + 6y²)

Question 34

Give the three rules for rearranging equations.

Answer 34

Do the same thing to both sides of the equation Do the inverse operation to get rid of things you don't want Keep going until the letter you want is on its own

Question 35

What is a function?

Answer 35

An expression that takes an input value, processes it and produces an output value

Question 36

How do you show x ÷ y using algebra notation?

Answer 36

x/y

Question 37

Given the formula m = 3n + 7 find m when n = 2

Answer 37

m = 3(2) + 7 m = 6 + 7 m = 13

Question 38

Expand and simplify (2x + 7)(3x - 4)

Answer 38

(2x + 7)(3x - 4) = 6x² - 8x + 21x - 28 = 6x² + 13x - 28

Question 39

A rectangle and a square have the same area. The rectangle has sides 4 cm and x cm long. The square has sides 6 cm long. Find x.

Answer 39

Area of the rectangle = 4x Area of the square = 36 4x = 36 x = 9