Daily Practice · Higher Plus
September 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1955 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1955Simplify sqrt(45) + sqrt(180), giving your answer in the form a sqrt(b).
- 2nd September 1955In an algebraic proof, how would you write an even number in terms of an integer n?
- 3rd September 1955A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 4th September 1955The 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.
- 5th September 1955A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 6th September 1955A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 7th September 1955A rectangle is 20 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th September 1955Make x the subject of 2x + 4 = y(x + 4).
- 9th September 1955y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 10th September 1955In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 11th September 1955The probability of winning a game is 1/2. A player expects 18 wins. How many games did they play?
- 12th September 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th September 1955Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 14th September 1955Write 2/(x + 1) + 5/(x - 2) as a single fraction.
- 15th September 1955y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 16th September 1955In a vector proof you find that vector PQ = 5a - b and vector RS = 25a - 5b. What does this show about PQ and RS?
- 17th September 1955A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 18th September 1955A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 19th September 1955A block has mass 480 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th September 1955Solve 9x^2 - 9x + 2 = 0.
- 21st September 1955y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 25.
- 22nd September 1955A cuboid measures 13 cm by 6 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd September 1955A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th September 1955On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th September 1955x = 166 and y = 108, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th September 1955f(x) = 2x + 6. Work out the inverse function f^-1(x).
- 27th September 1955A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 28th September 1955A cuboid measures 4 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th September 1955A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th September 1955A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?