Dr Frost Year 7 Revision Dr Frost Round

ζ Dr Frost Year 7 Revision

ζ Dr Frost Round 1 – Negative Numbers

ζ Dr Frost Round 2 – Sequences

The following is a sequence: 2 5 8 11 14 17 … Find a formula that gives the nth term in the sequence. ?

The following is a sequence: 2 5 8 11 14 17 … Give you’ve found the formula 3 n – 1 in the previous question, what is the 40 th term in the sequence? ?

The following is a sequence: 9 8 7 6 5 4 … Find a formula that gives the nth term in the sequence. ?

ζ Dr Frost Round 3 – Straight Lines

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

What is the equation of this line? y 3 x

What is the equation of this line? y x

Which of the following is not an equation of the line? y x -2

ζ Dr Frost Round 4 – Forming and solving equations

Two rectangles of equal size are put together to make a shape. The perimeter of this shape is 300. What is its area? y 2 y

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!)

ζ Dr Frost Round 5 – Squares, multiples, LCM, GCD

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

What is the prime factorisation of 60? ?

What is the Greatest Common Divisor of 10 and 15? ?

What is the Greatest Common Divisor of 126 and 180? ?

What is the Lowest Common Multiple of 8 and 12? ?

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

ζ Dr Frost Round 6 – Fractions

Fractions ? ?

Converting between fractions/decimals/%s Decimal 0. 01 0. 05 0. 125 0. 333. . . 0. 5 0. 6 0. 7 0. 875 1 Fraction 1/100? 1/20 ? 1/10 ? 1/8 ? 1/5 ? 1/4 ? 1/3 ? 1/2 ? 3/5 ? 7/10 ? 4/5 ? 7/8 ? 1 ? Percentage 1% ? 5% ? 10%? ? 12. 5% 20%? 25%? 33. 33% ? 50%? 60%? 70%? 87. 5% ? 100% ?

Converting fractions to recurring decimals Work these out to 5 dp by using long division. 4 9 ? = 0. 44444. . . 3 7 ? = 0. 42857. . . 3 ? = 0. 27272. . . 11

Percentages A car’s value depreciates by 20%. Its original value was £ 15, 500. Find its new value. Method 1 – Find the decrease and subtract Method 2 – Use a ‘decimal multiplier’ The ‘non calculator’ method The ‘calculator’ method 10% of £ 15, 500 is £ 1, 550 So 20% is £ 3100 ? £ 15, 500 - £ 3, 100 = £ 12, 400 £ 15, 500 x 0. 8 = £ 12, 400 ?

Angles Show that x=y+z y z 150° ? x 30° 70° 60° ? 75° ? 40°

Perimeter and Area ? 2 Area = 65 cm ? 2 Area = 44 cm ? Perimeter = 32 cm 8 cm 5 cm 16 cm 10 cm 5 cm 4 cm 14 cm 5 cm

Circles 4 Area of shaded region = 4 –? π 12 Area = 4π ? Perimeter = 8 +? 2π 4 Area = 18π ? Perimeter = 12 +? 6π

BIDMAS Fully bracket these expressions based on the order of operations: ? ? ? ?

ζ Dr Frost Transformations

8 Question 1 6 Describe this transformation. Object 4 Image 2 -10 -8 -6 -4 -2 2 -2 ? -4 A reflection in the line y = x. -6 4 6 8 10

Question 2 A point (3, 4) is translated by the vector -2 ( 2 ). What is the resulting point? (1, ? 6)

Question 3 8 We’re rotating the given shape 90° clockwise about the point (-1, 1). Given the point P on the object, what will 6 be the corresponding point on the image? P 4 2 -10 -8 -6 -4 -2 2 4 6 -2 A: (1, 2) B: (0, 3) -4 -6 C: (3, 2) D: (1, 3) 8 10

Question 4 Give the equation of these four lines. 6 4 x =? 0 8 x ? = y 2 -10 -8 -6 -4 -2 y =? 0 2 -2 -4 -6 4 y= 6 ? - x 8 10

Question 5 A -10 -8 -6 8 I reflect the blue object in the line y = x followed by reflecting it in the y-axis. What’s the resulting image? 6 4 B C -4 2 -2 D 2 4 6 8 -2 E Answer: B ? -4 -6 10

8 Question 6 I 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. 6 4 After first reflection. 2 -10 -8 -6 -4 -2 2 -2 -4 ? Rotation 90° clockwise about the origin. -6 4 6 8 10 After second reflection.

8 Question 7 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 Object 10

8 Question 7 Fully describe this transformation, using a single transformation. Object -10 -8 -6 6 4 2 -4 -2 2 -2 -4 Rotation 90° clockwise about the point (-3, -2)? -6 Image 4 6 8 10

8 Question 8 Fully describe this transformation, using a single transformation. Image -10 -8 -6 6 4 2 -4 -2 2 -2 -4 Rotation 90° anticlockwise about the point? (-4, -2) -6 Object 4 6 8 10

8 Question 9 Fully describe this transformation, using a single transformation. Image -10 -8 -6 6 4 2 -4 -2 2 -2 -4 Rotation 180° about the point ? (1, -1) -6 Object 4 6 8 10

8 Question 7 6 4 2 -10 -8 -6 -4 -2 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. 2 4 6 8 -2 -4 -6 Object 10