Daily Practice · Higher Plus
October 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2007The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2nd October 2007A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 3rd October 2007A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 4th October 2007Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
- 5th October 2007Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 6th October 2007y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 9.
- 7th October 2007In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 8th October 2007The probability of winning a game is 1/5. A player expects 3 wins. How many games did they play?
- 9th October 2007On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th October 2007A rectangle is 30 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th October 2007f(x) = 5x + 6 and g(x) = 2x - 1. Work out fg(1).
- 12th October 2007A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 13th October 2007In a vector proof you find that vector PQ = 3a + 2b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 14th October 2007A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 15th October 2007A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 16th October 2007Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 17th October 2007The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 18th October 2007y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 19th October 2007A cuboid measures 4 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th October 2007A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st October 2007On 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?
- 22nd October 2007A block has mass 200 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd October 2007A quadratic sequence starts 6, 6, 8, 12. Work out the second difference, and the coefficient of n^2.
- 24th October 2007y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 25th October 2007A cuboid measures 11 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th October 2007A bag holds 7 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th October 2007A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 28th October 2007x = 91 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th October 2007Solve x^2 - 11x + 18 < 0.
- 30th October 2007y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 49.
- 31st October 2007The 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.