Daily Practice · Higher Plus
June 1966 5-a-day
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The batch download puts all 5 tiers' June 1966 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1966y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 2nd June 1966A cuboid measures 7 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd June 1966A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th June 1966A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 5th June 1966x = 171 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th June 1966Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 7th June 1966y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 64.
- 8th June 1966The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 9th June 1966A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 10th June 1966On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th June 1966A car covers 820 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th June 1966f(x) = 3x + 6 and g(x) = 6x + 2. Work out fg(-3).
- 13th June 1966A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 14th June 1966In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 15th June 1966The probability of winning a game is 3/10. A player expects 18 wins. How many games did they play?
- 16th June 1966A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 17th June 1966Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 18th June 1966The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 19th June 1966y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 20th June 1966In a vector proof you find that vector PQ = a + 2b and vector RS = 5a + 10b. What does this show about PQ and RS?
- 21st June 1966A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 22nd June 1966On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd June 1966Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).
- 24th June 1966A quadratic sequence starts 11, 20, 35, 56. Work out the second difference, and the coefficient of n^2.
- 25th June 1966y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 26th June 1966A cuboid measures 10 cm by 7 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th June 1966A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th June 1966A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 29th June 1966A rectangle is 4 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th June 1966Solve x^2 + 4x + 3 > 0.