Daily Practice · Higher Plus
June 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1959 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1959Work out the nth term of the quadratic sequence 8, 22, 42, 68, ...
- 2nd June 1959A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd June 1959A cuboid measures 8 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th June 1959A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th June 1959A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 6th June 1959A car covers 600 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th June 1959The point (-6, -5) lies on y = f(x). Write down its image on y = f(x - 6).
- 8th June 1959y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 9th June 1959A cuboid measures 13 cm by 4 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th June 1959A bag holds 5 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th June 1959On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th June 1959Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 13th June 1959Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 14th June 1959y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 15th June 1959The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 16th June 1959A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 17th June 1959A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 18th June 1959Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 19th June 1959f(x) = 6x - 3 and g(x) = 6x + 3. Work out fg(3).
- 20th June 1959y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 64.
- 21st June 1959In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 22nd June 1959The probability of winning a game is 1/4. A player expects 3 wins. How many games did they play?
- 23rd June 1959On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th June 1959A rectangle is 16 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th June 1959The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 26th June 1959A train slows steadily from 17 m/s to rest in 10 seconds. Work out its deceleration.
- 27th June 1959In a vector proof you find that vector PQ = 4a + 4b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 28th June 1959A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th June 1959A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 30th June 1959Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).