ζYear 7 RevisionDr Frost

ζRound 1 – Negative NumbersDr Frost

6−6−5

3×(−2)

−1010−7

(−5)×(−2)

5−61

3+(−2)

−11−5

(−3 )−2

−3−742

(−5 )−(−2)

ζRound 2 – SequencesDr Frost

3𝑛−1

The following is a sequence:

2 5 8 11 14 17 …

Find a formula that gives the nth term in the sequence.

?

119

The following is a sequence:

2 5 8 11 14 17 …

Give you’ve found the formula 3n – 1 in the previous question, what is the 40th term in the sequence?

?

−𝑛+10𝑜𝑟 10−𝑛

The following is a sequence:

9 8 7 6 5 4 …

Find a formula that gives the nth term in the sequence.

?

ζRound 3 – Straight LinesDr Frost

𝑦=𝑥𝑥+𝑦=0𝑦−𝑥=0

Which of the following is not the equation of this line?

x

y

𝑥=3𝑦=3𝑦=𝑥+3

What is the equation of this line?

x

y

3

𝑦=𝑥𝑦=−𝑥𝑥− 𝑦=0

What is the equation of this line?

x

y

𝑦=−2𝑦+2=0𝑦−2=0

Which of the following is not an equation of the line?

x

y

-2

ζRound 4 – Forming and solving equationsDr Frost

6

Solve:

?

𝑥=7

Solve:

?

𝑥=−12

Solve:

?

𝑧=2

Solve:

?

200025003600

Two rectangles of equal size are put together to make a shape. The perimeter of this shape is 300. What is its area?

y

2y

222324

I take my age, triple it, and add 4. This is four times the age I was 7 years ago. How old am I?(Solve it using algebra!)

ζRound 5 – Squares, multiples, LCM, GCDDr Frost

3𝑛2−23𝑛+13 (𝑛+1)

Which of these is always divisible by 3 for any integer n?

22×3×5

What is the prime factorisation of 60?

?

5

What is the Greatest Common Divisor of 10 and 15?

?

18

What is the Greatest Common Divisor of 126 and 180?

?

24

What is the Lowest Common Multiple of 8 and 12?

?

36

What is the first square number (except 1) that is also a triangular number?

?

ζRound 6 – FractionsDr Frost

?

?

?

?

?

?

Fractions

Converting between fractions/decimals/%s

0.010.050.10.1250.20.250.333...0.50.60.70.80.8751

1/1001/201/101/81/51/41/31/23/57/104/57/81

1%5%10%12.5%20%25%33.33%50%60%70%80%87.5%100%

Decimal Fraction Percentage

?????????????

?????????????

Converting fractions to recurring decimals

37

49

311

Work these out to 5dp by using long division.

= 0.44444...

= 0.42857...

= 0.27272...

?

?

?

Percentages

A car’s value depreciates by 20%. Its original value was £15,500. Find its new value.

10% of £15,500 is £1,550So 20% is £3100

£15,500 - £3,100 = £12,400

Method 1 – Find the decrease and subtract Method 2 – Use a ‘decimal multiplier’

£15,500 x 0.8 = £12,400

The ‘non calculator’ method The ‘calculator’ method

??

Angles

x

y

z

Show that x = y + z

75°30°

150°

?

?

70°40°

60°?

Perimeter and Area

5cm

10cm16cm

Area = 65cm2?

14cm

8cm

5cm4cm

Area = 44cm2?

5cm

Perimeter = 32cm?

Circles

12

Area = 18π

Perimeter = 12 + 6π 4

Area = 4π

Perimeter = 8 + 2π

?? ?

?

Area of shaded region = 4 – π

4

?

BIDMASFully bracket these expressions based on the order of operations:

A trick question! There is no bracketing, since addition and subtraction don’t have precedence over eachother. We’d evaluate left to right, (i.e. subtract b first, then add c) and DEFINITELY NOT

Suppose . Bob evaluates as 100. Explain what Bob did wrong.He multiplied 5 by 2 and then squared the result. But by BIDMAS, he should have squared the 2 first, and then multiplied by 5. The correct result is 20.

?

?

?

?

ζTransformationsDr Frost

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 1Describe this transformation.

A reflection in the line y = x.?

Object

Image

Question 2

A point (3,4) is translated by the vector ( ). What is the resulting point?

(1, 6)?

-22

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 3 We’re rotating the given shape 90° clockwise about the point (-1, 1). Given the point P on the object, what will be the corresponding point on the image?

P

A: (1,2) B: (0,3) C: (3,2) D: (1,3)

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 4

y = x

y = -x

y = 0

x =

0

?

?

Give the equation of these four lines.

??

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 5

AB C

D

EAnswer:B?

I reflect the blue object in the line y = x followed by reflecting it in the y-axis. What’s the resulting image?

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 6I reflect my object in the line y = x, followed by a reflection in the x-axis.Describe a single transformation that would have resulted in the same image.

Rotation 90° clockwise about the origin.?

After first reflection.

After second reflection.

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 7Translate this shape by the vector

Object

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 7Fully describe this transformation, using a single transformation.

Object

Rotation 90° clockwise about the point (-3,-2)?

Image

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 8Fully describe this transformation, using a single transformation.

Image

Rotation 90° anticlockwise about the point (-4,-2)?

Object

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 9Fully describe this transformation, using a single transformation.

Image

Rotation 180° about the point (1,-1) ?

Object

-10 -8 -6 -4 -2 2 4 6 8 10

8

6

4

2

-2

-4

-6

Question 7Rotate the shape 90 anticlockwise about the point .

Object

Remember to focus on one point at a time, to count squares, and use ‘common sense’ the check your point looks roughly in the right place.