Daily Practice · Higher Plus
August 1962 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1962 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1962A rectangle is 9 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd August 1962Solve x^2 - 3x - 4 > 0.
- 3rd August 1962y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 4th August 1962In 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.
- 5th August 1962The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
- 6th August 1962On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th August 1962Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 8th August 1962Write x^2 - 10x - 2 in the form (x + a)^2 + b.
- 9th August 1962y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 10th August 1962In a vector proof you find that vector PQ = 4a - 2b and vector RS = 8a - 4b. What does this show about PQ and RS?
- 11th August 1962A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 12th August 1962A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 13th August 1962A block has mass 670 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th August 1962Work out the coordinates of the turning point of y = x^2 + 10x + 4.
- 15th August 1962y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 81.
- 16th August 1962A cuboid measures 13 cm by 15 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th August 1962A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th August 1962On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th August 1962x = 166 and y = 120, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th August 1962Simplify (x^2 + 7x + 10)/(x + 5).
- 21st August 1962A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd August 1962A cuboid measures 13 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd August 1962A bag holds 5 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th August 1962A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 25th August 1962A car covers 400 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th August 1962In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 27th August 1962y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 28th August 1962The 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.
- 29th August 1962A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 30th August 1962On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st August 1962Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.