Daily Practice · Higher Plus
November 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1957 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1957Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 2nd November 1957Solve x^2 - 2x - 15 > 0.
- 3rd November 1957A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
- 4th November 1957In a vector proof you find that vector PQ = a - 3b and vector RS = 3a - 9b. What does this show about PQ and RS?
- 5th November 1957A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 6th November 1957A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 7th November 1957Simplify sqrt(45) + sqrt(125), giving your answer in the form a sqrt(b).
- 8th November 1957Write x^2 - 16x + 11 in the form (x + a)^2 + b.
- 9th November 1957y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 10th November 1957A cuboid measures 4 cm by 7 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th November 1957A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th November 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th November 1957A rectangle is 28 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th November 1957Work out the coordinates of the turning point of y = x^2 - 12x - 1.
- 15th November 1957y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 16th November 1957A cuboid measures 5 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th November 1957A bag holds 3 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th November 1957A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 19th November 1957Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 20th November 1957Simplify (x^2 + 6x - 16)/(x - 2).
- 21st November 1957y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
- 22nd November 1957The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 23rd November 1957A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 24th November 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th November 1957A block has mass 700 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th November 1957In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
- 27th November 1957A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 28th November 1957In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 29th November 1957The probability of winning a game is 3/5. A player expects 36 wins. How many games did they play?
- 30th November 1957A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?