Daily Practice · Higher Plus
June 1960 5-a-day
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The batch download puts all 5 tiers' June 1960 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1960In an algebraic proof, how would you write an even number in terms of an integer n?
- 2nd June 1960y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 3rd June 1960A cuboid measures 6 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th June 1960A bag holds 4 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th June 1960On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th June 1960A block has mass 420 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th June 1960Make x the subject of 4x + 4 = y(x + 4).
- 8th June 1960y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 9th June 1960The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 10th June 1960A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 11th June 1960A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 12th June 1960x = 97 and y = 21, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th June 1960Write 2/(x - 6) + 4/(x + 3) as a single fraction.
- 14th June 1960y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 64.
- 15th June 1960In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 16th June 1960The probability of winning a game is 1/2. A player expects 40 wins. How many games did they play?
- 17th June 1960On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th June 1960A car covers 110 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th June 1960Solve 12x^2 + 19x + 5 = 0.
- 20th June 1960A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 21st June 1960In a vector proof you find that vector PQ = 2a - 5b and vector RS = 8a - 20b. What does this show about PQ and RS?
- 22nd June 1960A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 23rd June 1960A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 24th June 1960Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
- 25th June 1960f(x) = 6x + 3. Work out the inverse function f^-1(x).
- 26th June 1960y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 27th June 1960A cuboid measures 4 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th June 1960A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th June 1960On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th June 1960Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).