Daily Practice · Higher Plus
July 1973 5-a-day
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The batch download puts all 5 tiers' July 1973 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1973The 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.
- 2nd July 1973A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 3rd July 1973On 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?
- 4th July 1973A rectangle is 7 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th July 1973Work out the coordinates of the turning point of y = x^2 + 2x + 9.
- 6th July 1973y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 7th July 1973In 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.
- 8th July 1973The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
- 9th July 1973A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 10th July 1973Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 11th July 1973Simplify (x^2 - 12x + 35)/(x - 7).
- 12th July 1973y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 49.
- 13th July 1973In a vector proof you find that vector PQ = 4a + 4b and vector RS = 8a + 8b. What does this show about PQ and RS?
- 14th July 1973A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 15th July 1973On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th July 1973A block has mass 330 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th July 1973In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 18th July 1973A train slows steadily from 38 m/s to rest in 5 seconds. Work out its deceleration.
- 19th July 1973A cuboid measures 3 cm by 7 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th July 1973A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st July 1973A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 22nd July 1973x = 39 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd July 1973Make x the subject of 8x + 4 = y(x + 4).
- 24th July 1973y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 25th July 1973A cuboid measures 14 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th July 1973A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th July 1973On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th July 1973A car covers 540 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.
- 29th July 1973Write 6/(x - 3) + 7/(x + 2) as a single fraction.
- 30th July 1973y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 31st July 1973The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.