Daily Practice · Higher Plus
September 1973 5-a-day
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The batch download puts all 5 tiers' September 1973 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1973On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd September 1973x = 159 and y = 106, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd September 1973The point (1, 2) lies on y = f(x). Write down its image on y = f(x) - 4.
- 4th September 1973A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 5th September 1973In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 6th September 1973The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 7th September 1973A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 8th September 1973A car covers 890 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th September 1973Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 10th September 1973y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 11th September 1973In a vector proof you find that vector PQ = 3a - b and vector RS = 9a - 3b. What does this show about PQ and RS?
- 12th September 1973A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 13th September 1973On 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?
- 14th September 1973Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 15th September 1973f(x) = 6x + 4 and g(x) = 2x - 4. Work out fg(4).
- 16th September 1973y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 17th September 1973A cuboid measures 15 cm by 13 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th September 1973A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th September 1973A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 20th September 1973Simplify sqrt(48) + sqrt(3), giving your answer in the form a sqrt(b).
- 21st September 1973The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 22nd September 1973y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 64.
- 23rd September 1973A cuboid measures 4 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th September 1973A bag holds 7 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th September 1973On 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?
- 26th September 1973A rectangle is 15 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th September 1973A quadratic sequence starts 2, 6, 14, 26. Work out the second difference, and the coefficient of n^2.
- 28th September 1973A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 29th September 1973The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 30th September 1973A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.