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.
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?
?
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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.
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