Daily Practice · Higher Plus
September 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1954 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1954Work out the nth term of the quadratic sequence 9, 21, 39, 63, ...
- 2nd September 1954y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 36.
- 3rd September 1954A cuboid measures 11 cm by 13 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th September 1954A bag holds 7 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th September 1954On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th September 1954A block has mass 870 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th September 1954The point (6, 3) lies on y = f(x). Write down its image on y = -f(x).
- 8th September 1954A train slows steadily from 28 m/s to rest in 8 seconds. Work out its deceleration.
- 9th September 1954The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 10th September 1954A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 11th September 1954A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 12th September 1954x = 114 and y = 94, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th September 1954Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 14th September 1954y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 15th September 1954In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 16th September 1954The probability of winning a game is 3/5. A player expects 15 wins. How many games did they play?
- 17th September 1954On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th September 1954A car covers 720 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.
- 19th September 1954f(x) = 5x - 4 and g(x) = 4x + 4. Work out fg(5).
- 20th September 1954y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 21st September 1954In a vector proof you find that vector PQ = 4a + 2b and vector RS = 16a + 8b. What does this show about PQ and RS?
- 22nd September 1954A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 23rd September 1954A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 24th September 1954Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 25th September 1954The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 26th September 1954y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 36.
- 27th September 1954A cuboid measures 10 cm by 7 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th September 1954A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th September 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th September 1954Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).