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26 cardsNECO Senior School Certificate Examination

NECO SSCE Mathematics and Science Core Concepts

Essential mathematical theorems, mensuration formulas, physics laws, and biological principles for NECO SSCE.

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Sum of Interior Angles of an n-Sided Polygon
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1
Sum of Interior Angles of an n-Sided Polygon
S = (n - 2) × 180° = (2n - 4) right angles. Each interior angle of a regular polygon: [(n - 2) × 180°] / n.
2
Circle Theorem: Angle at Center vs Circumference
The angle subtended by an arc at the center of a circle is twice the angle subtended by it at any point on the remaining circumference: ∠AOB = 2 × ∠APB.
3
Circle Theorem: Cyclic Quadrilateral
Opposite interior angles of a cyclic quadrilateral are supplementary (sum to 180°): ∠A + ∠C = 180° and ∠B + ∠D = 180°.
4
Alternate Segment Theorem
The angle between a tangent and a chord drawn through the point of contact equals the angle subtended by the chord in the alternate segment.
5
Volume and Curved Surface Area of a Cylinder
Volume: V = π r² h.
Curved Surface Area: CSA = 2π r h.
Total Surface Area (closed): TSA = 2π r(r + h).
6
Volume and Surface Area of a Right Cone
Volume: V = (1/3)π r² h.
Curved Surface Area: CSA = π r l (where l = √(r² + h²)).
Total Surface Area: TSA = π r(l + r).
7
Volume and Surface Area of a Sphere and Hemisphere
Sphere: Volume = (4/3)π r³, Surface Area = 4π r².
Solid Hemisphere: Volume = (2/3)π r³, Total Surface Area = 3π r².
8
Distance and Midpoint Formulas in Coordinate Geometry
Distance: d = √[(x2 - x1)² + (y2 - y1)²].
Midpoint: M = ((x1 + x2)/2, (y1 + y2)/2).
9
Gradient and Perpendicular Lines
Gradient: m = (y2 - y1) / (x2 - x1).
Parallel lines: m1 = m2.
Perpendicular lines: m1 × m2 = -1 (m2 = -1/m1).
10
Sine Rule for Triangles
a / sin A = b / sin B = c / sin C = 2R (where R is the circumradius).
11
Cosine Rule for Triangles
To find a side: a² = b² + c² - 2bc cos A.
To find an angle: cos A = (b² + c² - a²) / (2bc).
12
Area of a Triangle Using Sine
Area = 0.5 a b sin C = 0.5 b c sin A = 0.5 a c sin B.
13
Arithmetic Progression (AP) Formulas
nth term: Tn = a + (n - 1)d.
Sum of first n terms: Sn = 0.5 n [2a + (n - 1)d] = 0.5 n (a + l).
14
Geometric Progression (GP) Formulas
nth term: Tn = a r^(n - 1).
Sum of first n terms: Sn = a(r^n - 1) / (r - 1) for r > 1.
Sum to infinity: S_inf = a / (1 - r) for |r| < 1.
15
Quadratic Roots: Sum and Product Relations
For ax² + bx + c = 0 with roots α and β:
Sum: α + β = -b / a.
Product: αβ = c / a.
Identity: α² + β² = (α + β)² - 2αβ.
16
Compound Interest Formula
A = P(1 + r/100)ⁿ, where A is the accumulated amount, P is the principal, r is the annual rate, and n is the number of years. Interest CI = A - P.
17
Photolysis of Water in Photosynthesis
Light energy absorbed by chlorophyll in thylakoids splits water: 2H₂O -> 4H⁺ + 4e⁻ + O₂. Oxygen is liberated as a byproduct.
18
Osmosis: Turgidity vs Plasmolysis in Plant Cells
In hypotonic solution (pure water), endosmosis makes cells turgid.
In hypertonic solution (concentrated salt/sugar), exosmosis causes water loss and plasmolysis.
19
Xylem vs Phloem Transport
Xylem: unidirectional upward transport of water and dissolved mineral salts from roots via transpiration pull.
Phloem: bidirectional translocation of manufactured sucrose and amino acids from leaves to sinks.
20
Mendelian Monohybrid and Dihybrid Phenotypic Ratios
Monohybrid F2 cross (Tt × Tt): 3 dominant : 1 recessive.
Dihybrid F2 cross (RrYy × RrYy): 9 dominant-dominant : 3 dominant-recessive : 3 recessive-dominant : 1 recessive-recessive.
21
Sickle Cell Hemoglobin Inheritance
HbA = normal allele, HbS = sickle cell allele.
AA = normal, AS = sickle cell trait carrier (resistant to severe falciparum malaria), SS = sickle cell anemia.
22
Rhesus Incompatibility Mechanism
Occurs when an Rh-negative mother carries an Rh-positive fetus. Sensitization at first birth produces anti-Rh IgG antibodies that cross the placenta to attack red blood cells of subsequent Rh-positive fetuses.
23
Ten Percent Law in Ecological Energy Pyramids
Only approximately 10% of energy stored in biomass at one trophic level is transferred to the next consecutive level; 90% is dissipated as metabolic heat and respiration.
24
Biological Vectors of Major African Tropical Diseases
Malaria: female Anopheles mosquito.
Sleeping sickness (trypanosomiasis): tsetse fly (Glossina).
River blindness (onchocerciasis): blackfly (Simulium).
Yellow fever / Dengue: Aedes aegypti mosquito.
25
Bile Function in Lipid Digestion
Secreted by liver, stored in gallbladder, released into duodenum. Contains bile salts that emulsify large fats into micro-droplets, increasing surface area for pancreatic lipase.
26
Ultrafiltration in the Human Nephron
Occurs in the renal corpuscle (Bowman's capsule and glomerulus). High hydrostatic pressure filters water, glucose, amino acids, and urea out of blood capillaries, retaining blood cells and large proteins.

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