Daily Practice · Higher Plus
August 1974 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1974 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1974In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 2nd August 1974The probability of winning a game is 3/5. A player expects 33 wins. How many games did they play?
- 3rd August 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th August 1974x = 45 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th August 1974Solve x^2 + 15x + 56 > 0.
- 6th August 1974A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 7th August 1974In a vector proof you find that vector PQ = 3a + 2b and vector RS = 9a + 6b. What does this show about PQ and RS?
- 8th August 1974A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 9th August 1974A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 10th August 1974A car covers 840 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.
- 11th August 1974Write x^2 - 16x + 10 in the form (x + a)^2 + b.
- 12th August 1974y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 13th August 1974A cuboid measures 5 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th August 1974A 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?
- 15th August 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th August 1974Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 17th August 1974Work out the coordinates of the turning point of y = x^2 + 8x - 6.
- 18th August 1974y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 19th August 1974A cuboid measures 13 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th August 1974A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st August 1974A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 22nd August 1974Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 23rd August 1974Simplify (x^2 - 4x - 12)/(x - 6).
- 24th August 1974y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
- 25th August 1974The 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.
- 26th August 1974A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 27th August 1974On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th August 1974A rectangle is 7 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th August 1974In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 30th August 1974A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 31st August 1974In 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.