Daily Practice · Higher Plus
June 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1963 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1963The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 2nd June 1963On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd June 1963A block has mass 880 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th June 1963Solve x^2 - 7x + 6 < 0.
- 5th June 1963A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 6th June 1963In a vector proof you find that vector PQ = a - b and vector RS = 5a - 5b. What does this show about PQ and RS?
- 7th June 1963A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 8th June 1963A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 9th June 1963x = 184 and y = 91, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th June 1963Write x^2 + 14x - 10 in the form (x + a)^2 + b.
- 11th June 1963y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 12th June 1963A cuboid measures 5 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th June 1963A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th June 1963On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th June 1963A car covers 650 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.
- 16th June 1963Work out the coordinates of the turning point of y = x^2 + 8x - 9.
- 17th June 1963y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 18th June 1963A cuboid measures 10 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th June 1963A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th June 1963A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 21st June 1963Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 22nd June 1963Simplify (x^2 + 5x - 14)/(x - 2).
- 23rd June 1963y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 24th June 1963The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 25th June 1963A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 26th June 1963On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th June 1963Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
- 28th June 1963In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 29th June 1963A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 30th June 1963In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.