Introduction to Algebra (OCR GCSE Maths: Higher): Exam Questions

The body mass index, $B$ , for a person of mass $m$ kg and height $h$ metres is given by the formula

$B=\frac{m}{h^2}$

Usman has a mass of 50 kg.
He has a height of 1.57 m.

Work out Usman's body mass index.
Give your answer correct to one decimal place.

Tom's height is 1.80m.
He wants his body mass index to be 21

Work out the mass that will give Tom a body mass index of 21.

$$\begin{gathered} A=4bc \\ A=100 \\ b=2 \end{gathered}$$

  Work out the value of  $c$.

You can change temperatures from °F to °C by using the formula

$C=\frac{5\left(F-32\right)}{9}$

$F$ is the temperature in °F.
$C$ is the temperature in °C.

The minimum temperature in an elderly person's home should be 20 °C.

Mrs Smith is an elderly person.
The temperature in Mrs Smith's home is 77 °F.

Decide whether or not the temperature in Mrs Smith's home is lower than the minimum temperature should be.

$x=0.7$

Work out the value of  $\frac{{\left(x+1\right)}^2}{2x}$
Write down all the figures on your calculator display.

$h=3t^2$ Work out the value of $h$ when $t=5$.

$h=3t^2$

Work out the value of $t$ when $h=108$

Make $a$ the subject of the formula

$v=u+at$

$h=5t^2+2$

i) Work out the value of $h$ when $t=-2$

[1]

ii) Work out a value of $t$ when $h=47$

[2]

Martina has answered some questions on algebra.
In each question, she has made an error.

Describe her error and give the correct answer to each problem.

Question 1       Simplify. 2a × a × a

         Martina’s answer 4a

Martina’s error is .......................................................................................................................

Correct answer = .........................................................

Question 2   Simplify.  $\frac{x^{10}}{x^2}$

Martina’s answer $x^5$

Martina’s error is .......................................................................................................................

Correct answer = ..........................................................

Question 3      $s=ut+\frac{1}{2}a{t}^2$

                Find $s$ when $u=0$, $t=5$ and $a=6$.   

Martina’s solution  $s=0\times 5+\frac{1}{2}\times 6\times 5^2$

   $s=0+{15}^2$

   $s=225$

Martina’s error is............................................................

Correct answer = ..........................................................

Find the value of $s$ when $u=12,$ $a=10$ and $t=4$.

$s=ut+\frac{1}{2}a{t}^2$

In a baking competition, 5 judges each give a cake a mark from 1 to 10.

The score for the cake is calculated using the formula

$S=4x+12$

where $x$ is the mean of the 5 marks.

Maya's cake gets the marks 6, 9, 7, 5 and 8.

Work out Maya's score.

Felix's cake gets a score of 40.

Felix says

My five marks must have been 6, 7, 7, 7 and 8 — that's how I got a mean of 7.

Explain why Felix is not necessarily correct, stating an example which disproves him.

$w=5y^2–y^3$

Work out the value of $w$ when $y=–2$

$w=$...................................................

$G=c^2–4c$

Find the value of $G$ when $c=–5$

$G=$ .........................................

Given that $a\times 60=b$  work out the value of $\frac{4b}{a}$

Simplify.

$2p-q-3q-5p$

$y=mx+c$  

Find the value of $y$ when $m=-3$, $x=-2$ and $c=-8$.  

$y=$ .................................................

$y=mx+c$.

Find the value of y when $m=-2$, $x=-7$ and $c=-3$.

$y=$ ..............................................

$s=ut+\frac{1}{2}a{t}^2$

Find the value of $s$ when $u=5.2,t=7$ and $a=1.6.$

$s=$ ................................................

Complete the statement.

When $5x=15$, $12x=$....................

$$\begin{gathered} y=p-2q{x}^2 \\ p=-10 \\ q=3 \\ x=-5 \end{gathered}$$

      Work out the value of $y$.

$\begin{array}{rcl}d& =& 2f\\ \frac{e-f}{d-e}& =& \frac{1}{4}\end{array}$

Work out the ratio $e:f$

$\frac{a}{b}=3c$

$\frac{b}{c}=2$

Work out the value of $a$ when $c=8$

$a$and $b$ are positive values.

Show that  $\frac{7a+2b-3a}{8a+6b+2a-b}$ always simplifies to the same value.

Amy has $x$ beads.

Billy has three more beads than Amy.

Carly has four times as many beads as Billy.

Circle the expression for the number of beads that Carly has.

Kelly is trying to work out the two values of w for which $3w-w^3=2$
Her values are 1 and -1

Are her values correct?
You must show your working.

$y=x^4-4x^3$

Find the value of $y$ when $x=-1$.

$y=$...............................................

$s=ut+\frac{1}{2}a{t}^2$

Find $s$ when $t=26.5,u=104.3,a=-2.2.$ 
Give your answer in standard form, correct to 4 significant figures.  

$s$ = ....................................................

One solution of the equation $a{x}^2+a=150$ is $x=7$.

Find the value of $a$.  

$a$ = ....................................................

Find the other solution.  

$x$ = .................................................... 

Work out the values of $a$ and $b$ in the identity

      $5(7x+8)+3(2x+b)=ax+13$

$a$ = .....................        $b$= .....................